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Nepal SEE Mathematics study materials
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Nepal SEE Mathematics practice questions

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Question 1Sets

If A = {x : x is an even natural number less than 10}, which roster form represents A?

  1. {2, 4, 6, 8, 10}
  2. {1, 2, 4, 6, 8}
  3. {2, 4, 6, 8} Correct answer.
  4. {0, 2, 4, 6, 8}

Explanation

The even natural numbers below 10 are 2, 4, 6 and 8. The number 10 is not less than 10, 0 is not a natural number in the SEE convention, and 1 is odd. Therefore the roster form contains exactly 2, 4, 6 and 8.

Question 2Sets

The set B is formed by the distinct letters of the word MATHEMATICS. What is n(B)?

  1. 7
  2. 8 Correct answer.
  3. 11
  4. 10

Explanation

The word MATHEMATICS has 11 letters in total, but M, A and T are repeated. The distinct letters are M, A, T, H, E, I, C and S, so the cardinal number n(B) is 8.

Question 3Sets

If U = {1, 2, 3, 4, 5, 6} and A = {2, 4, 6}, what is A'?

  1. {1, 3, 5} Correct answer.
  2. {1, 3, 5, 6}
  3. {2, 4, 6}
  4. {1, 2, 3, 4, 5, 6}

Explanation

The complement A' consists of all elements of the universal set U that are not in A. Removing 2, 4 and 6 from U leaves 1, 3 and 5. Hence A' = {1, 3, 5}.

Question 4Sets

How many proper subsets does a set with 5 elements have?

  1. 30
  2. 25
  3. 32
  4. 31 Correct answer.

Explanation

A set with 5 elements has 2^5 = 32 subsets in total. A proper subset is any subset except the set itself, so subtract 1. Thus the number of proper subsets is 32 - 1 = 31.

Question 5Sets

For two sets A and B, n(A) = 20, n(B) = 15 and n(A ∪ B) = 28. What is n(A ∩ B)?

  1. 7 Correct answer.
  2. 5
  3. 35
  4. 8

Explanation

The inclusion-exclusion formula gives n(A ∪ B) = n(A) + n(B) - n(A ∩ B). Substituting the values gives 28 = 20 + 15 - n(A ∩ B), so n(A ∩ B) = 35 - 28 = 7.

Question 6Sets

In a class of 40 students, 25 like mathematics, 20 like science, and 10 like both subjects. How many students like neither mathematics nor science?

  1. 15
  2. 5 Correct answer.
  3. 10
  4. 35

Explanation

The number who like at least one subject is 25 + 20 - 10 = 35. Since there are 40 students in the class, the number who like neither subject is 40 - 35 = 5.

Question 7Sets

Which set-builder notation exactly describes the set {1, 3, 5, 7, 9}?

  1. {x : x is a prime number less than 10}
  2. {x : x is a natural number less than 10}
  3. {x : x is an odd natural number less than 10} Correct answer.
  4. {x : x is an odd natural number less than 10 and greater than 1}

Explanation

The given roster contains the odd natural numbers below 10, namely 1, 3, 5, 7 and 9. The notation must therefore require both oddness and being less than 10. Including an extra condition such as greater than 1 would wrongly remove 1 from the set.

Question 8Sets

If A = {x : x is a factor of 12} and B = {x : x is a factor of 18}, what is A ∩ B?

  1. {1, 2, 3, 6} Correct answer.
  2. {1, 2, 3, 4, 6}
  3. {1, 2, 3, 4, 6, 9, 12, 18}
  4. {6}

Explanation

The factors of 12 are 1, 2, 3, 4, 6 and 12, while the factors of 18 are 1, 2, 3, 6, 9 and 18. Their common factors are 1, 2, 3 and 6, so A ∩ B = {1, 2, 3, 6}.

Question 9Sets

In a survey of 100 people, 60 read a Nepali newspaper, 45 read an English newspaper, and 20 read both newspapers. How many read exactly one newspaper?

  1. 85
  2. 80
  3. 25
  4. 65 Correct answer.

Explanation

People who read only Nepali number 60 - 20 = 40. People who read only English number 45 - 20 = 25. Therefore, the number who read exactly one newspaper is 40 + 25 = 65.

Question 10Sets

Let U = {1, 2, 3, ..., 12}, A = {x : x is a multiple of 2} and B = {x : x is a multiple of 3}. What is (A ∪ B)'?

  1. {1, 5, 7, 11, 12}
  2. {1, 5, 7, 11} Correct answer.
  3. {1, 5, 11}
  4. {1, 5, 7}

Explanation

A = {2, 4, 6, 8, 10, 12} and B = {3, 6, 9, 12}, so A ∪ B = {2, 3, 4, 6, 8, 9, 10, 12}. Removing these from U leaves 1, 5, 7 and 11, so (A ∪ B)' = {1, 5, 7, 11}.

Question 11Sets

If A = {2, 3, 4, 5} and B = {4, 5, 6}, which set represents A − B?

  1. {2, 3} Correct answer.
  2. {2, 3, 6}
  3. {6}
  4. {4, 5}

Explanation

The difference A − B contains only the elements that are in A but not in B. Removing 4 and 5, which also belong to B, leaves 2 and 3. The element 6 is not in A, so it cannot appear in A − B.

Question 12Sets

Which pair of sets is equal?

  1. {p, q, r} and {p, q, r, s}
  2. {a, b, c} and {c, a, b} Correct answer.
  3. {2, 4, 6, 8} and {2, 4, 6}
  4. {1, 2, 3} and {1, 2}

Explanation

Two sets are equal when they contain exactly the same elements, regardless of the order in which those elements are written. The sets {a, b, c} and {c, a, b} both contain a, b and c and no other elements. Therefore they are equal sets.

Question 13Sets

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {x : x is a prime number less than 10}. Which set is A′?

  1. {1, 4, 6, 8, 9, 10} Correct answer.
  2. {1, 2, 3, 5, 7, 8}
  3. {2, 3, 5, 7, 9, 10}
  4. {4, 6, 7, 8, 9, 10}

Explanation

The prime numbers less than 10 are 2, 3, 5 and 7, so A = {2, 3, 5, 7}. The complement A′ consists of all elements of U that are not in A. Thus A′ = {1, 4, 6, 8, 9, 10}, and note that 1 is included because it is not prime.

Question 14Sets

How many subsets of A = {1, 2, 3, 4} contain the element 2?

  1. 16
  2. 4
  3. 8 Correct answer.
  4. 15

Explanation

Every subset containing 2 is formed by taking 2 together with any subset of the remaining three elements {1, 3, 4}. A set with three elements has 2^3 = 8 subsets. Therefore, exactly 8 subsets of A contain 2.

Question 15Sets

For two sets A and B, n(A) = 18, n(B) = 14 and n(A − B) = 10. What is n(A ∩ B)?

  1. 6
  2. 10
  3. 12
  4. 8 Correct answer.

Explanation

The elements of A are split into those that are only in A and those that are in both A and B. Since n(A) = 18 and n(A − B) = 10, the number in both sets is 18 − 10 = 8. Hence n(A ∩ B) = 8.

Question 16Sets

In a survey of 60 students, 35 like tea, 30 like coffee and 15 like both drinks. How many students like exactly one of the two drinks?

  1. 15
  2. 20
  3. 50
  4. 35 Correct answer.

Explanation

The number who like tea only is 35 − 15 = 20, and the number who like coffee only is 30 − 15 = 15. Adding these gives the number who like exactly one drink: 20 + 15 = 35. The 15 students who like both are excluded from this count.

Question 17Sets

Which roster form represents C = {x : x ∈ N, x is a multiple of 4 and 10 < x < 25}?

  1. {12, 16, 20, 24} Correct answer.
  2. {10, 14, 18, 22}
  3. {12, 16, 24, 28}
  4. {12, 16, 20, 28}

Explanation

The multiples of 4 greater than 10 and less than 25 are 12, 16, 20 and 24. The numbers 28 and above are outside the stated range, and numbers such as 10, 14, 18 and 22 are not multiples of 4. Therefore C = {12, 16, 20, 24}.

Question 18Sets

Which set is equal to {x : x is a positive integer, x^2 < 30}?

  1. {1, 2, 3, 4, 5} Correct answer.
  2. {1, 2, 3, 4, 5, 6}
  3. {2, 3, 4, 5}
  4. {1, 2, 3, 4}

Explanation

For positive integers, 1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16 and 5^2 = 25 are all less than 30. However, 6^2 = 36 is not less than 30, so 6 is excluded. Thus the set is {1, 2, 3, 4, 5}.

Question 19Sets

In a school, 60% of the students like mathematics, 50% like science, and 20% like both. If 12 students like neither mathematics nor science, how many students are in the school?

  1. 120 Correct answer.
  2. 100
  3. 60
  4. 150

Explanation

The percentage who like at least one subject is 60 + 50 − 20 = 90%. Hence the percentage who like neither is 100 − 90 = 10%. Since 10% of the students is 12, the total number of students is 12 ÷ 0.10 = 120.

Question 20Sets

In a survey of 100 students, 50 like mathematics, 40 like science, 30 like English, 15 like mathematics and science, 10 like science and English, 8 like mathematics and English, and 5 like all three subjects. How many like at least one of the three subjects?

  1. 97
  2. 87
  3. 100
  4. 92 Correct answer.

Explanation

Using inclusion-exclusion for three sets, n(M ∪ S ∪ E) = 50 + 40 + 30 − 15 − 10 − 8 + 5. The sum is 120 − 33 + 5 = 92. Therefore 92 students like at least one of the three subjects.

Question 21Sets

For the set A = {m, n}, which set represents the power set P(A)?

  1. {{m}, {n}, {m, n}, {n, m}}
  2. {∅, {m, n}}
  3. {∅, {m}, {n}, {m, n}} Correct answer.
  4. {m, n, {m}, {n}}

Explanation

The power set of A is the set of all its subsets, and every set has ∅ and itself as subsets. A set with 2 elements has 2² = 4 subsets, so P(A) = {∅, {m}, {n}, {m, n}}. Each member of a power set must itself be a set, written inside braces.

Question 22Sets

Which of the following pairs of sets is disjoint?

  1. C = {2, 4, 6} and D = {1, 3, 5} Correct answer.
  2. A = {1, 2, 3} and B = {3, 4, 5}
  3. E = {0, 1} and F = {1, 2}
  4. G = {5, 6} and H = {6, 7}

Explanation

Two sets are disjoint when their intersection is the empty set, that is, they share no element. The even numbers {2, 4, 6} and the odd numbers {1, 3, 5} have nothing in common, so C ∩ D = ∅.

Question 23Sets

Let U = {1, 2, 3, ..., 15}, A = {x : x is a prime number} and B = {x : x is an even number}. Which set represents A ∩ B′?

  1. {5, 7, 11, 13}
  2. {3, 5, 7, 11, 13} Correct answer.
  3. {3, 5, 7}
  4. {2, 3, 5, 7, 11, 13}

Explanation

The primes in U are 2, 3, 5, 7, 11 and 13, while B′ is the set of odd numbers in U since B is the even numbers. Keeping only the primes that are odd leaves {3, 5, 7, 11, 13}; the prime 2 is removed because it is even.

Question 24Sets

Which set-builder notation represents the set {−3, −2, −1, 0, 1, 2, 3}?

  1. {x : x ∈ W, −3 ≤ x ≤ 3}
  2. {x : x ∈ Z, −3 < x < 3}
  3. {x : x ∈ N, −3 ≤ x < 3}
  4. {x : x ∈ Z, −3 ≤ x ≤ 3} Correct answer.

Explanation

The set contains every integer from −3 to 3 inclusive, so the variable must range over the integers Z and both endpoints must be included using ≤. The notation {x : x ∈ Z, −3 ≤ x ≤ 3} produces exactly the seven listed numbers.

Question 25Sets

In a class of 60 students, 30 study Nepali, 25 study English and 20 study Mathematics. Also, 10 study Nepali and English, 8 study English and Mathematics, 6 study Nepali and Mathematics, and 4 study all three subjects. How many students study exactly two subjects?

  1. 8
  2. 12 Correct answer.
  3. 16
  4. 24

Explanation

Each pairwise figure includes the 4 students who study all three subjects, so subtract 4 from every pair to get those studying exactly that pair. This gives (10 − 4) + (8 − 4) + (6 − 4) = 6 + 4 + 2 = 12 students studying exactly two subjects.

Question 26Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A shopkeeper in Bhaktapur buys a brass statue for Rs 1,200 and sells it for Rs 1,500. What is his profit percent?

  1. 33.33%
  2. 30%
  3. 25% Correct answer.
  4. 20%

Explanation

Profit is the selling price minus the cost price, so here it is Rs 1,500 − Rs 1,200 = Rs 300. Profit percent in business arithmetic is always calculated on the cost price, giving (300 ÷ 1,200) × 100 = 25%.

Question 27Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A cooperative in Chitwan lends Rs 8,000 at 10% per annum simple interest for 3 years. How much interest does the borrower pay in total?

  1. Rs 800
  2. Rs 2,400 Correct answer.
  3. Rs 2,640
  4. Rs 3,200

Explanation

For simple interest, use I = P × T × R / 100 = 8,000 × 3 × 10 / 100 = Rs 2,400. In this method interest is charged only on the original principal, so the interest of each year stays the same.

Question 28Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A customer buys a pressure cooker marked at Rs 2,000 before tax in Nepal. Charging value added tax at the standard rate fixed by the government, how much must the customer pay in total?

  1. Rs 2,600
  2. Rs 2,260 Correct answer.
  3. Rs 2,300
  4. Rs 2,130

Explanation

The standard rate of value added tax in Nepal is 13%, so the tax on Rs 2,000 is 13% of 2,000 = Rs 260. VAT is added to the price before tax, so the customer pays 2,000 + 260 = Rs 2,260.

Question 29Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A printing machine worth Rs 50,000 is insured against depreciation charged at 10% per annum on the reducing balance. What is its value after 2 years?

  1. Rs 40,000
  2. Rs 45,000
  3. Rs 44,000
  4. Rs 40,500 Correct answer.

Explanation

Reducing-balance depreciation applies the rate to the value left at the start of each year, so value after 2 years = 50,000 × (1 − 10/100)² = 50,000 × 0.81. This gives Rs 40,500, which is more than the Rs 40,000 obtained by taking a flat 10% of the original cost each year.

Question 30Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A money exchanger in Kathmandu quotes: buying rate for 1 US dollar = NRs 132.50 and selling rate = NRs 133.20. A tourist hands over 500 US dollars in cash and receives Nepali rupees. How many rupees does the tourist get?

  1. NRs 65,750
  2. NRs 67,250
  3. NRs 66,600
  4. NRs 66,250 Correct answer.

Explanation

When a customer gives foreign currency to the exchanger, the exchanger is buying that currency, so the buying rate applies. The amount is 500 × 132.50 = NRs 66,250; using the selling rate here would wrongly give the tourist more rupees than the exchanger allows.

Question 31Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

The marked price of a school bag is Rs 4,000. A shop allows 15% discount and then adds 13% VAT on the discounted price. What amount does the buyer finally pay?

  1. Rs 3,400
  2. Rs 3,952
  3. Rs 4,520
  4. Rs 3,842 Correct answer.

Explanation

Discount is worked out on the marked price first: 15% of 4,000 = Rs 600, leaving Rs 3,400. VAT is then charged on that reduced price, 13% of 3,400 = Rs 442, so the buyer pays 3,400 + 442 = Rs 3,842.

Question 32Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A person's taxable income for a year is Rs 6,00,000. The slabs are: 5% on the first Rs 3,00,000, 10% on the next Rs 2,00,000 and 20% on the remaining amount. What is the annual income tax?

  1. Rs 60,000
  2. Rs 50,000
  3. Rs 45,000
  4. Rs 55,000 Correct answer.

Explanation

Income tax under slabs is charged step by step, not at one rate on the whole income. First Rs 3,00,000 at 5% = Rs 15,000, next Rs 2,00,000 at 10% = Rs 20,000, and the remaining Rs 1,00,000 at 20% = Rs 20,000, giving Rs 55,000 in total.

Question 33Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A sum of Rs 4,500 earns Rs 1,350 simple interest in 3 years. At what rate per annum is the interest being paid?

  1. 10% Correct answer.
  2. 12%
  3. 9%
  4. 6%

Explanation

Rearranging I = P × T × R / 100 gives R = 100I / (P × T). Substituting the values, R = (100 × 1,350) / (4,500 × 3) = 1,35,000 / 13,500 = 10% per annum.

Question 34Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

The difference between the compound interest and the simple interest on a sum at 10% per annum for 2 years is Rs 50. What is the sum?

  1. Rs 5,000 Correct answer.
  2. Rs 10,000
  3. Rs 2,500
  4. Rs 4,000

Explanation

For two years the gap between compound and simple interest is the interest earned in the second year on the first year's interest, so it equals P × (R/100)². Here 50 = P × (10/100)² = 0.01P, giving P = Rs 5,000; checking, CI = 1,050 and SI = 1,000.

Question 35Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A student in Pokhara must pay a fee of 2,500 US dollars to a foreign university. The bank's selling rate is NRs 134.80 per US dollar and it charges a commission of 0.5% on the rupee amount. How much Nepali currency must the student arrange?

  1. NRs 335,315
  2. NRs 337,000
  3. NRs 340,370
  4. NRs 338,685 Correct answer.

Explanation

To send foreign currency the bank is selling dollars, so the selling rate applies: 2,500 × 134.80 = NRs 337,000. The commission of 0.5% on this amount is Rs 1,685, and adding it gives 337,000 + 1,685 = NRs 338,685, which is what the student must pay.

Question 36Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A fruit seller in Dharan sells a crate of oranges for Rs 2,760 and makes a profit of 15%. What was the cost price of the crate?

  1. Rs 2,346
  2. Rs 2,500
  3. Rs 3,174
  4. Rs 2,400 Correct answer.

Explanation

Profit percent is taken on the cost price, so the selling price is 115% of the cost price. Cost price = 2760 ÷ 1.15 = Rs 2,400.

Question 37Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A farmer borrows Rs 12,000 from a savings cooperative at 8% per annum simple interest. How many years will it take for the interest to amount to Rs 3,840?

  1. 3 years
  2. 4 years Correct answer.
  3. 2.5 years
  4. 5 years

Explanation

Simple interest is P × R × T ÷ 100. Here 3,840 = 12,000 × 8 × T ÷ 100 = 960T, so T = 4 years.

Question 38Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A trekking guide in Kathmandu receives 500 US dollars from a tourist. The bank's buying rate is NRs 130.20 per US dollar and its selling rate is NRs 131.00. How many Nepalese rupees will the guide receive when exchanging the dollars at the bank?

  1. NRs 66,000
  2. NRs 65,500
  3. NRs 64,100
  4. NRs 65,100 Correct answer.

Explanation

When a bank buys US dollars from a customer, it applies the buying rate, here NRs 130.20 per dollar. Therefore 500 × 130.20 = NRs 65,100.

Question 39Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

The price tag of a mobile phone in a Kathmandu showroom is Rs 33,900 including 13% VAT. What is the amount of VAT included in the price?

  1. Rs 4,000
  2. Rs 3,900 Correct answer.
  3. Rs 3,000
  4. Rs 4,407

Explanation

A VAT-inclusive price equals the pre-VAT price times 1.13. The pre-VAT price is 33,900 ÷ 1.13 = Rs 30,000, so VAT = 33,900 − 30,000 = Rs 3,900.

Question 40Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A youth club in Butwal deposits Rs 25,000 in a bank that pays 12% per annum compound interest, compounded yearly. What amount will the club receive at the end of 2 years?

  1. Rs 28,000
  2. Rs 30,000
  3. Rs 31,360 Correct answer.
  4. Rs 31,000

Explanation

For yearly compounding, amount = P(1 + R/100)^T. Thus 25,000(1.12)^2 = 25,000 × 1.2544 = Rs 31,360.

Question 41Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A shopkeeper's annual taxable income is Rs 7,20,000. The tax rates are 5% on the first Rs 3,00,000, 10% on the next Rs 2,00,000, and 20% on the remaining amount. What is the total income tax?

  1. Rs 72,000
  2. Rs 64,000
  3. Rs 85,000
  4. Rs 79,000 Correct answer.

Explanation

Tax on the first Rs 3,00,000 is 5% = Rs 15,000; on the next Rs 2,00,000 it is 10% = Rs 20,000; the remaining Rs 2,20,000 is taxed at 20% = Rs 44,000. Total tax = 15,000 + 20,000 + 44,000 = Rs 79,000.

Question 42Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A retailer marks a jacket at Rs 3,200 and allows a 20% discount. If he still makes a profit of 25% on the cost price, what is the cost price of the jacket?

  1. Rs 2,400
  2. Rs 2,048 Correct answer.
  3. Rs 2,560
  4. Rs 2,000

Explanation

After a 20% discount, selling price = 3,200 × 0.80 = Rs 2,560. Since this is 25% above cost price, cost price = 2,560 ÷ 1.25 = Rs 2,048.

Question 43Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A cooperative lends Rs 40,000 at 10% per annum compounded semi-annually. What is the compound interest for one year?

  1. Rs 4,100 Correct answer.
  2. Rs 4,000
  3. Rs 4,410
  4. Rs 4,200

Explanation

Semi-annual compounding means the 10% annual rate is halved to 5% per half-year, and one year has two periods. Amount = 40,000(1.05)^2 = Rs 44,100, so compound interest = 44,100 − 40,000 = Rs 4,100.

Question 44Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

The difference between compound interest and simple interest on a sum at 10% per annum for 3 years is Rs 620. What is the sum?

  1. Rs 22,000
  2. Rs 20,000 Correct answer.
  3. Rs 18,000
  4. Rs 25,000

Explanation

For 3 years at 10%, CI − SI = P(0.10)^2(3 + 0.10) = 0.031P. Setting 0.031P = 620 gives P = 620 ÷ 0.031 = Rs 20,000.

Question 45Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A trader sells two bicycles for Rs 9,000 each. On one he gains 20% and on the other he loses 20%. What is his overall result?

  1. 4% profit
  2. 4% loss Correct answer.
  3. 5% loss
  4. No profit, no loss

Explanation

Cost of the first bicycle = 9,000 ÷ 1.20 = Rs 7,500; cost of the second = 9,000 ÷ 0.80 = Rs 11,250. Total cost = Rs 18,750 and total selling price = Rs 18,000, so loss = Rs 750, which is 750/18,750 × 100 = 4%.

Question 46Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A retailer in Biratnagar buys a ceiling fan for Rs 1,800 and sells it at a loss of 12%. What is the selling price of the fan?

  1. Rs 1,584 Correct answer.
  2. Rs 1,616
  3. Rs 2,016
  4. Rs 1,764

Explanation

Loss percent is calculated on the cost price, so the loss is 12% of Rs 1,800, which equals Rs 216. Subtract this loss from the cost price: Rs 1,800 minus Rs 216 gives Rs 1,584. A selling price below cost price means the retailer has made a loss.

Question 47Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A teacher in Hetauda deposits Rs 15,000 in a bank that pays 9% per annum simple interest. What total amount will she receive after 2 years?

  1. Rs 17,700 Correct answer.
  2. Rs 18,000
  3. Rs 17,250
  4. Rs 16,350

Explanation

Simple interest is calculated as P × T × R ÷ 100, so the interest is Rs 15,000 × 2 × 9 ÷ 100 = Rs 2,700. Add this interest to the principal: Rs 15,000 + Rs 2,700 = Rs 17,700. The question asks for the total amount, not just the interest.

Question 48Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A sum of money invested at 10% per annum compound interest, compounded yearly, amounts to Rs 7,260 in 2 years. What is the principal?

  1. Rs 5,800
  2. Rs 6,500
  3. Rs 6,000 Correct answer.
  4. Rs 6,200

Explanation

For compound interest, amount = P(1 + R/100)^T. Here P = 7,260 ÷ (1.10)^2 = 7,260 ÷ 1.21 = Rs 6,000. Checking: Rs 6,000 grows to Rs 6,600 after one year and Rs 7,260 after two years at 10% compound interest.

Question 49Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A small hotel in Pokhara has annual sales revenue of Rs 12,00,000 and allowable expenses of Rs 4,50,000. If income tax is charged at 20% on the taxable profit, what is the tax payable?

  1. Rs 1,50,000 Correct answer.
  2. Rs 2,40,000
  3. Rs 1,60,000
  4. Rs 1,40,000

Explanation

Taxable profit is sales revenue minus allowable expenses: Rs 12,00,000 − Rs 4,50,000 = Rs 7,50,000. Income tax is 20% of this taxable profit, so tax = 20% of Rs 7,50,000 = Rs 1,50,000. Expenses must be deducted before applying the tax rate.

Question 50Arithmetic (profit and loss, simple and compound interest, tax, currency exchange)

A money exchanger in Kathmandu quotes: buying rate for 1 US dollar = NRs 132.00 and selling rate = NRs 132.80; buying rate for 1 euro = NRs 145.00 and selling rate = NRs 146.00. A trader wants to convert 500 US dollars into euros through the exchanger. How many euros will he receive, rounded to two decimal places?

  1. EUR 450.68
  2. EUR 452.05 Correct answer.
  3. EUR 455.17
  4. EUR 451.25

Explanation

The exchanger first buys the 500 US dollars at the buying rate of NRs 132.00, giving 500 × 132.00 = NRs 66,000. To give euros, the exchanger sells euros at the selling rate of NRs 146.00, so the trader receives 66,000 ÷ 146 = EUR 452.05 when rounded to two decimal places. Using the euro buying rate would be incorrect because the trader is buying euros from the exchanger.