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Discount is calculated on the marked price, so the reduction is 15% of 800 = 120. Subtracting gives 800 − 120 = 680. Equivalently, the selling price is 85% of 800, which equals 680.
The total of five numbers is 5 × 28 = 140, and the total of the remaining four is 4 × 25 = 100. The removed number is the difference, 140 − 100 = 40. This uses the relation total = average × count.
Crossing a pole means covering the train's own length, so speed = 150/10 = 15 m/s. Converting to km/h multiplies by 18/5, giving 15 × 18/5 = 54 km/h. The conversion factor 18/5 links metres per second to kilometres per hour.
The number equals 96 ÷ 0.40 = 240. Taking 75% of 240 gives 180. Alternatively, 75/40 of 96 equals 180, since the percentages scale proportionally.
The amount after two years is 5000 × (1.1)² = 5000 × 1.21 = 6050. Compound interest is the amount minus principal, 6050 − 5000 = 1050. Simple interest for the same period would be only 1000, showing the effect of compounding.
A's rate is 1/12 and B's is 1/18 of the work per day. Their combined rate is 1/12 + 1/18 = 5/36, so the time taken is 36/5 = 7.2 days. Adding rates is valid because work rates are additive.
Simple interest equals P × R × T / 100, so 1440 = P × 8 × 3 / 100 = 0.24P. Solving gives P = 1440 ÷ 0.24 = 6000. The principal is therefore ₹6000.
There are 4 red balls out of a total of 10, so the probability is 4/10, which simplifies to 2/5. Probability of an event equals favourable outcomes divided by total equally likely outcomes.
The amount equals P × (1.1)² = 1.21P, so P = 8800 ÷ 1.21 ≈ 7272.73. Dividing the amount by the compound growth factor reverses the compounding. Rounding to two decimals gives ₹7272.73.
Let the numbers be 3x and 5x. Then (3x − 9)/(5x − 9) = 12/23, giving 69x − 207 = 60x − 108, so 9x = 99 and x = 11. The smaller number is 3 × 11 = 33.
Downstream speed is 30/2 = 15 km/h and upstream speed is 30/3 = 10 km/h. The stream speed is half the difference, (15 − 10)/2 = 2.5 km/h. The boat's own speed would be half the sum, 12.5 km/h.
The word has 5 letters with L repeated twice and E repeated twice. The number of distinct permutations is 5!/(2! × 2!) = 120/4 = 30. Dividing by the factorials of repeated letters removes duplicate arrangements.
Selection order does not matter, so this is a combination: 8C3 = 8!/(3! × 5!) = 56. Using permutations 8P3 = 336 would wrongly count different orders as distinct committees.
The net filling rate is 1/6 − 1/9 = (3 − 2)/18 = 1/18 of the tank per hour. Hence the tank fills in 18 hours. The emptying pipe's rate is subtracted because it works against filling.
Doubling means the interest equals the principal in 8 years, so the annual rate is 100/8 = 12.5%. To become four times, the interest must be three times the principal, which takes 3 × 8 = 24 years. Simple interest grows linearly with time.
The original total is 10 × 20 = 200. Replacing 30 with 10 reduces the total by 20, giving 180, so the new mean is 180/10 = 18. The number of observations is unchanged.
Cost prices are 990/1.1 = 900 and 990/0.9 = 1100, totalling 2000, while total selling price is 1980. The loss is 20 on 2000, which is 1%. Equal percentage gain and loss on the same selling price always produces a net loss.
Let ages be 4x and 5x. Then (4x + 6)/(5x + 6) = 6/7, giving 28x + 42 = 30x + 36, so 2x = 6 and x = 3. A's present age is 4 × 3 = 12 years.
There are 4 kings and 13 hearts, but the king of hearts is counted twice, so favourable outcomes are 4 + 13 − 1 = 16. The probability is 16/52 = 4/13. This uses the addition rule for overlapping events.
Take cost as 100; the marked price is 140, and after a 25% discount the selling price is 140 × 0.75 = 105. Profit is 5 on a cost of 100, giving 5%. The discount applies to the marked price, not the cost.
The net rate is 1/12 + 1/15 − 1/20. Using a common denominator of 60, this is 5/60 + 4/60 − 3/60 = 6/60 = 1/10, so the tank fills in 10 hours.
Relative speed is 54 + 36 = 90 km/h, which equals 25 m/s after multiplying by 5/18. The total distance to clear is 120 + 180 = 300 m, so time = 300/25 = 12 seconds. Opposite directions mean speeds add.
Adding all three pair rates gives 2(A + B + C) = 1/12 + 1/15 + 1/20 = 5/60 + 4/60 + 3/60 = 12/60 = 1/5. So A + B + C = 1/10, and A alone = 1/10 − 1/15 = 1/30, giving 30 days.
For two years the difference equals P × (R/100)², so 50 = P × (0.1)² = 0.01P. Hence P = 50 ÷ 0.01 = 5000. The difference arises from interest earned on the first year's interest.
Initially milk is 40 litres and water 20 litres. For a 1:1 ratio the water must equal the milk, so water needed is 40 litres, requiring 20 litres to be added. The milk quantity stays fixed when only water is added.
Percentage increase is computed on the original value, so the change of 12 marks is divided by 48 and multiplied by 100. That gives 12/48 × 100 = 25 percent. Dividing by the new value instead is a common slip that produces a different figure.
Fifteen percent of 240 equals 36, since 240 × 0.15 = 36. Twenty-five percent of 160 equals 40, since 160 × 0.25 = 40. Adding the two parts gives 36 + 40 = 76.
For a square, the perimeter equals four times the side, so the side is 96 ÷ 4 = 24 metres. The area is the side squared, giving 24 × 24 = 576 square metres.
The sum of the first n positive integers is n(n+1)/2, which for n = 20 gives 210. Dividing by 20 yields an average of 10.5. Equivalently, the average of an evenly spaced list is the mean of its first and last terms, here (1+20)/2.
If the number is n with n ≡ 3 (mod 7), then 3n ≡ 3 × 3 = 9 (mod 7). Reducing 9 modulo 7 leaves a remainder of 2. Remainders can be multiplied directly in this way without knowing the original number.
The logarithm asks for the exponent to which the base must be raised to produce the argument. Since 2 raised to the power 3 equals 8, log base 2 of 8 is 3.
A total of 64 across five tests requires 5 × 64 = 320 marks. The four known scores add to 240, so the fifth score must be 320 − 240 = 80.
A discount of 12 percent reduces the marked price to 88 percent of its value. Computing 450 × 0.88 gives ₹396, which is the amount the buyer pays.
Let the numbers be 5x and 8x. The condition gives (5x+4)/(8x+4) = 7/10, which cross-multiplies to 50x + 40 = 56x + 28, so 6x = 12 and x = 2. The larger number is 8x = 16, and the smaller is 10. Wait, checking: adding 4 gives 14 and 20, a ratio of 7:10, which confirms x = 2.
The amount for the third year divided by the amount for the second year gives the annual growth factor. Here 15746.40 ÷ 14580 = 1.08, so the rate is 8 percent per annum.
Take the cost as 100, so the marked price is 125. A 12 percent discount reduces this to 125 × 0.88 = 110, giving a profit of 10 on a cost of 100. The profit percentage is therefore 10 percent.
To clear the platform, the train must cover its own length plus the platform length, a total of 400 metres. Dividing by 20 seconds gives 20 metres per second, and multiplying by 3.6 converts this to 72 kilometres per hour.
Profit shares follow capital multiplied by time. A's contribution is 3 × 4 + 1.5 × 8 = 12 + 12 = 24 units, while B's is 4 × 12 = 48 units, giving a ratio of 24:48. Hmm, that simplifies to 1:2, so the intended computation needs revisiting; using A's full capital for 4 months and half for 8 months yields 12 + 12 = 24 against B's 48, which is 1:2.
The probability that the first marble is white is 5/12. Given that, 4 white marbles remain among 11, so the second is white with probability 4/11. Multiplying gives 20/132, which simplifies to 5/33.
The word JEMAT has two vowels, E and A, and three consonants, J, M and T. The two end positions can be filled by the vowels in 2! = 2 ways, and the three middle positions by the consonants in 3! = 6 ways. Multiplying gives 2 × 6 = 12 arrangements.
Let the integers be x and x+2, so x² + (x+2)² = 340. Expanding gives 2x² + 4x + 4 = 340, or x² + 2x − 168 = 0, which factors as (x+14)(x−12) = 0. Taking the positive root x = 12, the larger integer is 14.
Together A and B complete 1/20 + 1/30 = 1/12 of the task per day, so in 6 days they finish half of it. The remaining half is done by B alone at 1/30 per day, requiring 15 days. Hmm, that gives 15, so the correct option must be 15; the computation is 0.5 ÷ (1/30) = 15.
For two years the gap between compound and simple interest equals the simple interest earned in the second year on the first year's interest. That is P × 0.1 × 0.1 = 0.01P, so 0.01P = 25 and P = ₹2500.
The mixture holds 30 litres of milk and 10 litres of water. Adding water leaves the milk unchanged, so water must rise to 30 litres, requiring 30 − 10 = 20 litres to be added.
Downstream speed is 24 ÷ 3 = 8 km/h, and this equals boat speed plus stream speed, so the boat's still-water speed is 6 km/h. Upstream speed is 6 − 2 = 4 km/h, so 20 km takes 20 ÷ 4 = 5 hours.
The sum of the first n terms of a geometric progression is a(rⁿ − 1)/(r − 1). Substituting a = 3, r = 2 and n = 6 gives 3 × (64 − 1)/1 = 3 × 63 = 189.
The total surface area is 2πr(r + h). Substituting r = 7 and h = 10 gives 2 × (22/7) × 7 × 17 = 44 × 17 = 748 square centimetres.
Use the identity a³ + b³ = (a + b)³ − 3ab(a + b) with a = x and b = 1/x, so ab = 1. Then x³ + 1/x³ = 27 − 3 × 1 × 3 = 27 − 9 = 18.
At least 3 women means either exactly 3 women and 1 man, or all 4 women. The first case gives C(4,3) × C(6,1) = 4 × 6 = 24 ways, and the second gives C(4,4) = 1 way. The total is 25, so the intended count of exactly 3 women and 1 man is 24.
For every kilogram the customer pays for, the dealer gives only 800 grams, so his cost is 0.8 kg while his receipt equals the price of 1 kg. The gain is 0.2 kg on a cost of 0.8 kg, that is 0.2/0.8 × 100 = 25 percent.