How many perfect squares lie between 1 and 1000?

The correct answer is B: 31. Perfect squares from 1 to 1000 are 1², 2², 3², ..., n² where n² ≤ 1000. So n ≤ √1000 ≈ 31.62. Therefore n can be 1, 2, 3, ..., 31. Total = 31 perfect squares.

A merchant's cost price is Rs. 800. He marks 40% above CP and gives 25% discount. His profit/loss percent is?

The correct answer is A: 5% profit. MP = 800 × 1.4 = 1120. SP = 1120 × 0.75 = 840. Profit = (840-800)/800 × 100 = 5%

A boat can cover 45 km downstream and 27 km upstream in 9 hours. If the speed of current is 3 km/h, find the speed of boat in still water.

The correct answer is A: 9 km/h. Let boat speed = b. Downstream = b+3, Upstream = b-3. (45/(b+3)) + (27/(b-3)) = 9. Solving: b = 9 km/h

A shopkeeper sells two items. Item A at 25% profit and Item B at 18% loss. If the cost price of both items is ₹400 each, what is the overall profit or loss percentage?

The correct answer is A: 3.5% profit. Step 1: Item A: SP = 400 + (25% of 400) = 400 + 100 = ₹500. Step 2: Item B: SP = 400 - (18% of 400) = 400 - 72 = ₹328. Step 3: Total CP = 800, Total SP = 828. Step 4: Profit% = (28/800) × 100 = 3.5%. So option A is correct.

Four numbers are in the ratio 1:2:3:4 with HCF = 7. Find their LCM.

The correct answer is B: 1680. Numbers are 7, 14, 21, 28. 7 = 7, 14 = 2 × 7, 21 = 3 × 7, 28 = 2² × 7. LCM = 2² × 3 × 7 = 4 × 3 × 7 × 2 = 1680.

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Quantitative Aptitude
Numbers

Quantitative aptitude questions for competitive exams

221 Q 7 Topics Take Mock Test

Difficulty: All Easy Medium Hard 81–90 of 221

Topics in Quantitative Aptitude

All Numbers 499 HCF and LCM 150 Profit and Loss 102 Time and Work 101 Percentage 101 Simple Interest 50 Average 48

Q.81 Medium Numbers

A merchant buys goods at Rs. 75 per unit and sells at Rs. 100 per unit. His profit per unit and overall profit percentage are?

A Rs. 25, 33.33%

B Rs. 25, 25%

C Rs. 20, 30%

D Rs. 30, 40%

Correct Answer: A. Rs. 25, 33.33%

EXPLANATION

Profit per unit = 100 - 75 = 25. Profit% = (25/75) × 100 = 33.33%

Test

Q.82 Medium Numbers

A can complete a work in 10 days. B can complete the same work in 15 days. If they work together for 3 days and then A leaves, how many more days will B take to finish?

A 5 days

B 6 days

C 7 days

D 8 days

Correct Answer: B. 6 days

EXPLANATION

Work rate A = 1/10, B = 1/15. Combined = 5/30 = 1/6. In 3 days = 3/6 = 1/2 work done. Remaining = 1/2. B's time = (1/2)/(1/15) = 7.5 days

Test

Q.83 Medium Numbers

A boat's speed in still water is 15 km/h. The speed of the current is 3 km/h. What is the time taken to travel 108 km downstream and return?

A 13.5 hours

B 14 hours

C 15 hours

D 16 hours

Correct Answer: C. 15 hours

EXPLANATION

When traveling downstream and upstream, the boat's effective speed changes due to the current's aid or resistance.

Step 1: Calculate Downstream Speed

Downstream, the current aids the boat's motion, so we add the current speed to the boat's speed in still water.

\text{Downstream speed} = \text{Boat speed} + \text{Current speed} = 15 + 3 = 18 \text{ km/h}

Step 2: Calculate Time for Downstream Journey

Using the formula: Time = Distance ÷ Speed, we find the time to travel 108 km downstream.

\text{Time (downstream)} = \frac{108}{18} = 6 \text{ hours}

Step 3: Calculate Upstream Speed

Upstream, the current opposes the boat's motion, so we subtract the current speed from the boat's speed in still water.

\text{Upstream speed} = \text{Boat speed} - \text{Current speed} = 15 - 3 = 12 \text{ km/h}

Step 4: Calculate Time for Upstream Journey

The boat must return the same 108 km against the current.

\text{Time (upstream)} = \frac{108}{12} = 9 \text{ hours}

Step 5: Calculate Total Time

Add the downstream and upstream times to get the total journey time.

\text{Total time} = 6 + 9 = 15 \text{ hours}

The answer is 15 hours.

Test

Q.84 Medium Numbers

A's income is 25% more than B's income. B's income is what percentage of A's income?

A 75%

B 80%

C 85%

D 90%

Correct Answer: B. 80%

EXPLANATION

If B = 100, then A = 125. B/A = 100/125 = 80%

Test

Q.85 Medium Numbers

A principal becomes Rs. 1331 in 3 years at 10% p.a. compound interest. What was principal?

A Rs. 1000

B Rs. 1050

C Rs. 1100

D Rs. 1200

Correct Answer: A. Rs. 1000

EXPLANATION

A = P(1.1)^3 = 1.331P = 1331. P = 1000

Test

Q.86 Medium Numbers

A product's price is reduced by 25% then increased by 25%. Net change is?

A 0% (no change)

B 6.25% decrease

C 6.25% increase

D 25% decrease

Correct Answer: B. 6.25% decrease

EXPLANATION

Let price = 100. After -25% = 75. After +25% of 75 = 75 × 1.25 = 93.75. Net decrease = 6.25%

Test

Q.87 Medium Numbers

A and B together can do work in 8 days. A alone can do it in 12 days. In how many days can B alone do it?

A 20 days

B 22 days

C 24 days

D 28 days

Correct Answer: C. 24 days

EXPLANATION

B's rate = 1/8 - 1/12 = (3-2)/24 = 1/24. B takes 24 days

Test

Q.88 Medium Numbers

A sells goods to B at 20% profit. B sells to C at 15% profit. C's cost price is Rs. 690. What is A's cost price?

A Rs. 500

B Rs. 550

C Rs. 575

D Rs. 600

Correct Answer: A. Rs. 500

EXPLANATION

C's CP = B's SP = 690. B's CP = 690/1.15 = 600. A's SP = B's CP = 600. A's CP = 600/1.2 = 500

Test

Q.89 Medium Numbers

A sum of Rs. 8000 becomes Rs. 9261 in 3 years at compound interest. What is the rate p.a.?

A 4%

B 5%

C 6%

D 7%

Correct Answer: B. 5%

EXPLANATION

A = P(1+r/100)^3. 9261 = 8000(1+r/100)^3. (1+r/100)^3 = 9261/8000 = 1.157625. 1+r/100 = 1.05. r = 5%

Test

Q.90 Medium Numbers

Two trains of lengths 120m and 180m cross each other in 10 seconds when moving towards each other. Their combined speed is?

A 54 km/h

B 108 km/h

C 162 km/h

D 90 km/h

Correct Answer: B. 108 km/h

EXPLANATION

Total distance = 120 + 180 = 300m. Combined speed = 300/10 = 30 m/s = 30 × 3.6 = 108 km/h

Test

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