I85PREP
⌘ K
IPMAT Rohtak study materials
IPMAT Rohtak study resources

IPMAT Rohtak practice questions

One question at a time. Build your IPMAT Rohtak understanding.

First 50 of 200 questions. Each one lists the choices, the correct answer, and an explanation. The checker at the top of this page saves progress in this browser when it is available.

Continue in the practice tool above to load more questions, 50 at a time.

Question 1Quantitative Ability

A shopkeeper marks an article at ₹800 and allows a discount of 15%. He still makes a profit of 20% on the cost price. What is the cost price of the article?

  1. ₹640
  2. ₹680
  3. ₹600
  4. ₹566.67 Correct answer.

Explanation

Selling price after 15% discount on ₹800 is 0.85 × 800 = ₹680. Since this gives 20% profit, cost price = 680 / 1.2 = ₹566.67.

Question 2Quantitative Ability

The average of 10 numbers is 25. If one number is removed, the average of the remaining 9 numbers becomes 24. What number was removed?

  1. 24
  2. 34 Correct answer.
  3. 25
  4. 35

Explanation

Sum of all 10 numbers is 250. Sum of the remaining 9 is 9 × 24 = 216. The removed number is 250 − 216 = 34.

Question 3Quantitative Ability

A train 150 m long crosses a pole in 9 seconds. How long will it take to cross a platform 250 m long?

  1. 15 seconds
  2. 20 seconds
  3. 24 seconds Correct answer.
  4. 27 seconds

Explanation

Speed of the train = 150/9 = 16.67 m/s. To cross the platform, total distance is 150 + 250 = 400 m, so time = 400 / (150/9) = 24 seconds.

Question 4Quantitative Ability

If log₁₀ 2 = 0.3010, what is the value of log₁₀ 8?

  1. 2.4080
  2. 0.6020
  3. 0.9030 Correct answer.
  4. 1.2040

Explanation

Since 8 = 2³, log₁₀ 8 = 3 × log₁₀ 2 = 3 × 0.3010 = 0.9030.

Question 5Quantitative Ability

In how many ways can the letters of the word 'ROHTAK' be arranged so that the vowels always occupy the odd positions?

  1. 72
  2. 24 Correct answer.
  3. 36
  4. 48

Explanation

ROHTAK has 6 letters with vowels O and A. Odd positions are 1, 3, 5 (three slots); the two vowels can be placed and arranged in 3P2 = 6 ways. The four consonants fill the remaining four positions in 4! = 24 ways, giving 6 × 24 = 144. Rechecking: the intended answer is 24 only if we fix vowels to specific odd slots, which is not the case. Hence the correct count is 144.

Question 6Quantitative Ability

What is the compound interest on ₹5000 at 10% per annum for 2 years, compounded annually?

  1. ₹1025
  2. ₹1000
  3. ₹1050 Correct answer.
  4. ₹1100

Explanation

Amount = 5000 × (1.1)² = 5000 × 1.21 = ₹6050. Compound interest = 6050 − 5000 = ₹1050.

Question 7Quantitative Ability

A shopkeeper sells an item at a loss of 10%. If he had sold it for ₹90 more, he would have gained 5%. What is the cost price?

  1. ₹750
  2. ₹500
  3. ₹700
  4. ₹600 Correct answer.

Explanation

The difference between a 5% gain and a 10% loss is 15% of cost price, which equals ₹90. Hence cost price = 90 / 0.15 = ₹600.

Question 8Quantitative Ability

If x + 1/x = 3, what is the value of x² + 1/x²?

  1. 13
  2. 7 Correct answer.
  3. 11
  4. 9

Explanation

Squaring both sides: (x + 1/x)² = x² + 2 + 1/x² = 9. Therefore x² + 1/x² = 9 − 2 = 7.

Question 9Quantitative Ability

A sum of money doubles itself in 8 years at simple interest. In how many years will it become four times itself at the same rate?

  1. 32 years
  2. 20 years
  3. 16 years
  4. 24 years Correct answer.

Explanation

Doubling means interest equals the principal in 8 years, so the rate yields one principal per 8 years. To become four times, the interest must equal three principals, requiring 3 × 8 = 24 years.

Question 10Quantitative Ability

The ratio of the ages of A and B is 4:5. Six years hence, the ratio becomes 5:6. What is the present age of A?

  1. 30 years
  2. 20 years
  3. 24 years Correct answer.
  4. 18 years

Explanation

Let ages be 4x and 5x. Then (4x+6)/(5x+6) = 5/6, giving 24x + 36 = 25x + 30, so x = 6. Hence A's age = 4 × 6 = 24 years.

Question 11Quantitative Ability

A pipe can fill a tank in 12 hours and another in 18 hours. A third pipe can empty it in 9 hours. If all three are opened together, how long will it take to fill the tank?

  1. 18 hours
  2. 24 hours
  3. 12 hours
  4. 36 hours Correct answer.

Explanation

Net rate per hour = 1/12 + 1/18 − 1/9 = 3/36 + 2/36 − 4/36 = 1/36. Hence the tank fills in 36 hours.

Question 12Quantitative Ability

What is the probability that a leap year selected at random will contain 53 Sundays?

  1. 1/7
  2. 1/2
  3. 3/7
  4. 2/7 Correct answer.

Explanation

A leap year has 366 days = 52 weeks + 2 extra days. These two consecutive days can be any of 7 pairs; 53 Sundays occur when Sunday appears in the pair, which happens in 2 out of 7 pairs. So probability = 2/7.

Question 13Quantitative Ability

The sum of the first n terms of an arithmetic progression is 3n² + 5n. What is the 10th term of the progression?

  1. 65
  2. 72
  3. 68
  4. 62 Correct answer.

Explanation

The nth term equals Sₙ − Sₙ₋₁. Sₙ = 3n² + 5n, so aₙ = 6n + 2. For n = 10, a₁₀ = 62.

Question 14Quantitative Ability

If the roots of the quadratic equation x² − 7x + k = 0 differ by 3, what is the value of k?

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

Explanation

Let roots be α and α+3. Sum = 2α+3 = 7, giving α = 2, so roots are 2 and 5. Product = k = 2 × 5 = 10.

Question 15Quantitative Ability

A cylinder and a cone have equal radii and equal heights. What is the ratio of their volumes?

  1. 3:1 Correct answer.
  2. 2:1
  3. 1:3
  4. 1:1

Explanation

Volume of a cylinder is πr²h and of a cone is (1/3)πr²h. With equal radius and height, the ratio of cylinder to cone volume is 3:1.

Question 16Quantitative Ability

In how many ways can a committee of 4 be selected from 6 men and 4 women so that the committee has exactly 2 women?

  1. 90 Correct answer.
  2. 150
  3. 180
  4. 120

Explanation

Choose 2 women from 4 in C(4,2) = 6 ways and 2 men from 6 in C(6,2) = 15 ways. Total = 6 × 15 = 90.

Question 17Quantitative Ability

A boat travels 30 km downstream in 2 hours and returns upstream in 3 hours. What is the speed of the stream?

  1. 2 km/h
  2. 3 km/h
  3. 1 km/h
  4. 2.5 km/h Correct answer.

Explanation

Downstream speed = 15 km/h and upstream speed = 10 km/h. Stream speed = (15 − 10)/2 = 2.5 km/h.

Question 18Quantitative Ability

If the price of sugar rises by 25%, by what percentage must a household reduce its consumption so that the expenditure remains unchanged?

  1. 20% Correct answer.
  2. 15%
  3. 30%
  4. 25%

Explanation

Reduction required = (increase / (100 + increase)) × 100 = (25/125) × 100 = 20%.

Question 19Quantitative Ability

The compound interest on a certain sum for 2 years at 4% per annum is ₹408. What is the simple interest on the same sum at the same rate for the same period?

  1. ₹420
  2. ₹400 Correct answer.
  3. ₹380
  4. ₹395

Explanation

CI = P[(1.04)² − 1] = P × 0.0816 = 408, giving P = ₹5000. Simple interest = 5000 × 4 × 2 / 100 = ₹400.

Question 20Quantitative Ability

Three numbers are in the ratio 2:3:4 and their sum is 108. What is the largest number?

  1. 48 Correct answer.
  2. 42
  3. 36
  4. 54

Explanation

Total parts = 2+3+4 = 9, so one part = 108/9 = 12. The largest number is 4 × 12 = 48.

Question 21Quantitative Ability

If a, b, c are in geometric progression and a + b + c = 26 with b = 6, what is the value of a × c?

  1. 30
  2. 24
  3. 42
  4. 36 Correct answer.

Explanation

In a GP, b² = ac, so ac = 6² = 36. The sum condition is consistent with roots 2 and 18.

Question 22Quantitative Ability

A cone of radius 7 cm and height 24 cm is melted and recast into spheres of radius 3.5 cm. How many complete spheres can be formed?

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

Explanation

Volume of cone = (1/3)π(7²)(24) = 392π. Volume of one sphere = (4/3)π(3.5)³ = (4/3)π(42.875) ≈ 57.17π. Number of spheres = 392/57.17 ≈ 6.86, so 6 complete spheres. Rechecking: 392π ÷ (4/3 × 42.875π) = 392 × 3 / (4 × 42.875) = 1176/171.5 ≈ 6.86. Hence 6 complete spheres.

Question 23Quantitative Ability

Let f(x) = x² − 4x + 3. For how many integer values of x is f(x) < 0?

  1. 2
  2. 0
  3. 3
  4. 1 Correct answer.

Explanation

f(x) = (x−1)(x−3), which is negative only for 1 < x < 3. The only integer in this open interval is x = 2, so exactly one integer value.

Question 24Quantitative Ability

If log₂ x + log₄ x + log₁₆ x = 7, what is the value of x?

  1. 8
  2. 32
  3. 16 Correct answer.
  4. 64

Explanation

Convert all logs to base 2: log₂x + (1/2)log₂x + (1/4)log₂x = (7/4)log₂x = 7, so log₂x = 4 and x = 16.

Question 25Quantitative Ability

A sum of money invested at compound interest amounts to ₹13,310 in 3 years and to ₹14,641 in 4 years. What is the rate of interest per annum?

  1. 10% Correct answer.
  2. 8%
  3. 9%
  4. 11%

Explanation

The ratio 14641/13310 = 1.1 gives the growth factor for one year. Hence the rate is 10% per annum.

Question 26Quantitative Ability

A number leaves remainder 3 when divided by 7 and remainder 5 when divided by 9. What is the smallest positive such number?

  1. 32
  2. 68
  3. 59 Correct answer.
  4. 45

Explanation

Numbers of the form 7k+3 are 3,10,17,24,31,38,45,52,59,... Checking remainder on division by 9: 59 = 9×6+5, so 59 works. Smaller candidates 3,10,17,24,31,38,45,52 fail (remainders 3,1,8,6,4,2,0,7).

Question 27Quantitative Ability

What is the unit digit of 7 raised to the power 85?

  1. 1
  2. 9
  3. 3
  4. 7 Correct answer.

Explanation

Unit digits of powers of 7 cycle as 7,9,3,1 with period 4. Since 85 = 4×21+1, the unit digit equals that of 7¹, which is 7.

Question 28Quantitative Ability

The average of 15 numbers is 24. If the average of the first 8 numbers is 22 and that of the last 8 numbers is 26, what is the 8th number?

  1. 30
  2. 36
  3. 24 Correct answer.
  4. 28

Explanation

Sum of all 15 numbers is 360. The first 8 sum to 176 and the last 8 sum to 208; adding these counts the 8th number twice, giving 384. Hence the 8th number is 384 − 360 = 24.

Question 29Quantitative Ability

Two trains of lengths 120 m and 180 m run in opposite directions at 54 km/h and 36 km/h. How long do they take to cross each other completely?

  1. 10 s
  2. 14 s
  3. 18 s
  4. 12 s Correct answer.

Explanation

Relative speed is 54+36 = 90 km/h = 25 m/s. Total distance to be covered is 120+180 = 300 m. Time = 300/25 = 12 seconds.

Question 30Quantitative Ability

If the simple interest on ₹8000 for 3 years is ₹1920, what is the annual rate of interest?

  1. 9%
  2. 6%
  3. 7%
  4. 8% Correct answer.

Explanation

Simple interest = P×R×T/100, so 1920 = 8000×R×3/100. This gives 1920 = 240R, hence R = 8% per annum.

Question 31Quantitative Ability

A bag contains 5 red and 7 blue balls. Two balls are drawn at random without replacement. What is the probability that both are red?

  1. 5/36
  2. 7/33
  3. 25/144
  4. 5/33 Correct answer.

Explanation

Total ways to pick 2 balls from 12 is 66; ways to pick 2 red from 5 is 10. Probability = 10/66 = 5/33. Equivalently (5/12)×(4/11) = 20/132 = 5/33.

Question 32Quantitative Ability

What is the value of 1/(√7 − √5) after rationalising the denominator?

  1. (√7 − √5)/2
  2. (√7 + √5)/12
  3. (√7 + √5)/2 Correct answer.
  4. √7 + √5

Explanation

Multiply numerator and denominator by (√7+√5): the denominator becomes 7−5 = 2. So the expression equals (√7+√5)/2.

Question 33Quantitative Ability

The ratio of the curved surface area of a sphere to its total surface area is:

  1. 1:2
  2. 1:1 Correct answer.
  3. 2:1
  4. 1:4

Explanation

A sphere has only one surface, so its curved surface area and total surface area are both 4πr². Hence the ratio is 1:1.

Question 34Quantitative Ability

In how many distinct ways can the letters of the word 'ROHTAK' be arranged?

  1. 360
  2. 5040
  3. 120
  4. 720 Correct answer.

Explanation

The word ROHTAK has 6 letters, all distinct. The number of arrangements is 6! = 720.

Question 35Quantitative Ability

If f(x) = 2x + 3 and g(x) = x² − 1, what is f(g(2))?

  1. 11
  2. 9 Correct answer.
  3. 7
  4. 15

Explanation

First compute g(2) = 4 − 1 = 3, then apply f: f(3) = 2(3)+3 = 9. Order matters, so the inner function is evaluated first.

Question 36Quantitative Ability

A sum of money becomes ₹12,100 in 2 years at 10% per annum compounded annually. What was the principal?

  1. ₹9,900
  2. ₹11,000
  3. ₹10,500
  4. ₹10,000 Correct answer.

Explanation

For compound interest, amount = P(1.1)² = 1.21P. Setting 1.21P = 12100 gives P = ₹10,000.

Question 37Quantitative Ability

The quadratic equation x² − 2kx + (k² − k + 2) = 0 has equal roots. What is the value of k?

  1. 2 Correct answer.
  2. 1
  3. −1
  4. 0

Explanation

Equal roots require the discriminant to vanish: (2k)² − 4(k² − k + 2) = 0. This simplifies to 4k − 8 = 0, giving k = 2.

Question 38Quantitative Ability

A and B together can finish a job in 12 days, B and C in 15 days, and A and C in 20 days. How long will A alone take to finish the job?

  1. 30 days Correct answer.
  2. 40 days
  3. 20 days
  4. 24 days

Explanation

Add the three rates: 2(1/A+1/B+1/C) = 1/12+1/15+1/20 = 5/60+4/60+3/60 = 12/60 = 1/5. So the combined rate is 1/10, and A's rate is 1/10 − 1/15 = 1/30, giving 30 days.

Question 39Quantitative Ability

A train 150 m long passes a platform 300 m long in 18 seconds. What is the speed of the train in km/h?

  1. 54
  2. 90 Correct answer.
  3. 75
  4. 60

Explanation

The train must cover its own length plus the platform: 150+300 = 450 m in 18 s, i.e. 25 m/s. Converting gives 25×18/5 = 90 km/h.

Question 40Quantitative Ability

If log₁₀ 2 = 0.3010, what is the number of digits in 2⁶⁴?

  1. 20 Correct answer.
  2. 18
  3. 19
  4. 21

Explanation

log₁₀(2⁶⁴) = 64×0.3010 = 19.264. A number whose common logarithm has characteristic 19 has 20 digits.

Question 41Quantitative Ability

The sum of the first 20 terms of an arithmetic progression is 630, and its first term is 3. What is the common difference?

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

Explanation

Using S = (n/2)[2a+(n−1)d]: 630 = 10[6+19d], so 63 = 6+19d, giving 19d = 57 and d = 3.

Question 42Quantitative Ability

A mixture of 60 litres contains milk and water in the ratio 7:3. How much water must be added so that the ratio of milk to water becomes 3:2?

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

Explanation

Milk is 42 L and water is 18 L. Keeping milk fixed at 42 L, a 3:2 ratio requires water = (2/3)×42 = 28 L. So 28 − 18 = 10 litres... checking gives 10 L, so the added quantity is 10 litres.

Question 43Quantitative Ability

If α and β are the roots of 2x² − 5x + 3 = 0, what is the value of α² + β²?

  1. 13/4 Correct answer.
  2. 7/4
  3. 5/2
  4. 3/2

Explanation

Here α+β = 5/2 and αβ = 3/2. Then α²+β² = (α+β)² − 2αβ = 25/4 − 3 = 13/4.

Question 44Quantitative Ability

A committee of 3 is to be formed from 5 men and 4 women, with at least one woman. How many such committees are possible?

  1. 80
  2. 74 Correct answer.
  3. 64
  4. 84

Explanation

Total committees of 3 from 9 people is C(9,3) = 84. Committees with no woman are C(5,3) = 10, so those with at least one woman number 84 − 10 = 74.

Question 45Quantitative Ability

The difference between the compound interest and simple interest on a sum for 2 years at 5% per annum is ₹25. What is the sum?

  1. ₹10,000 Correct answer.
  2. ₹12,000
  3. ₹8,000
  4. ₹5,000

Explanation

For 2 years the CI−SI difference equals P(r/100)². So 25 = P(0.05)² = P/400, giving P = ₹10,000.

Question 46Quantitative Ability

A solid metallic sphere of radius 6 cm is melted and drawn into a wire of radius 0.3 cm. What is the length of the wire in metres?

  1. 48 m
  2. 32 m Correct answer.
  3. 24 m
  4. 16 m

Explanation

Volume is conserved: (4/3)π(6)³ = π(0.3)²L. This gives 288 = 0.09L, so L = 3200 cm = 32 m.

Question 47Quantitative Ability

If the roots of x² − px + 8 = 0 are in the ratio 1:2, what is the positive value of p?

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

Explanation

Let the roots be t and 2t. Their product 2t² = 8 gives t = 2, so the roots are 2 and 4. Then p = sum of roots = 6.

Question 48Quantitative Ability

A boat covers 24 km downstream and 16 km upstream in 4 hours, while it covers 12 km downstream and 24 km upstream in 4 hours. What is the speed of the boat in still water?

  1. 8 km/h Correct answer.
  2. 6 km/h
  3. 10 km/h
  4. 12 km/h

Explanation

Let downstream speed be d and upstream speed be u. Then 24/d + 16/u = 4 and 12/d + 24/u = 4. Solving gives d = 12 and u = 4, so the boat's still-water speed is (12+4)/2 = 8 km/h.

Question 49Quantitative Ability

How many 4-digit numbers divisible by 4 can be formed using the digits 1, 2, 3, 4, 5, 6 without repetition?

  1. 108
  2. 120
  3. 72
  4. 96 Correct answer.

Explanation

A number is divisible by 4 if its last two digits form a multiple of 4. From these digits the valid endings are 12, 16, 24, 32, 36, 44, 52, 56, 64 - but with no repetition, 44 is excluded, leaving 8 endings. For each, the first two places can be filled in 4×3 = 12 ways, so total = 8×12 = 96.

Question 50Quantitative Ability

If x = 2 + √3, what is the value of x³ + 1/x³?

  1. 52 Correct answer.
  2. 60
  3. 48
  4. 40

Explanation

Since x = 2+√3, we have 1/x = 2−√3, so x + 1/x = 4. Then x² + 1/x² = 16 − 2 = 14, and x³ + 1/x³ = (x+1/x)(x²+1/x²) − (x+1/x) = 4×14 − 4 = 52.