A and B working together can complete a job in 6 days. B and C working together can complete it in 9 days. A and C working together can complete it in 12 days. In how many days can all three complete it together?

The correct answer is B: 7.2 days. 1/A + 1/B = 1/6. 1/B + 1/C = 1/9. 1/A + 1/C = 1/12. Adding: 2(1/A + 1/B + 1/C) = 1/6 + 1/9 + 1/12 = 6/36 + 4/36 + 3/36 = 13/36. 1/A + 1/B + 1/C = 13/72. Time = 72/13 ≈ 5.54 days. (Recalculating: 1/6 + 1/9 + 1/12. LCM=36. 6/36 + 4/36 + 3/36 = 13/36. So 2(1/A+1/B+1/C) = 13/36. Combined = 13/72. But th

A merchant purchased goods for ₹5000. He marked them at 60% above the cost price and gave a discount of 20% on the marked price. What is his profit percentage?

The correct answer is A: 28%. Step 1: CP = ₹5000. Step 2: Marked Price = 5000 + (60% of 5000) = 5000 + 3000 = ₹8000. Step 3: Discount = 20% of 8000 = ₹1600. Step 4: SP = 8000 - 1600 = ₹6400. Step 5: Profit% = (1400/5000) × 100 = 28%. So option A is correct.

The ratio of cost price to marked price of an item is 3:5. If a discount of 20% is given, what is the profit percentage?

The correct answer is D: 33.33%. Let CP = 3x, MP = 5x. SP = 5x × 0.8 = 4x. Profit = 4x - 3x = x. Profit% = x/3x × 100 = 33.33%.

If 75 workers can build a wall in 120 days, how many days will 90 workers take?

The correct answer is C: 100 days. Work = Workers × Days = 75 × 120 = 9000. Days = 9000/90 = 100 days.

The profit on 50 units is ₹2,500. What is the average profit per unit if 200 units are sold?

The correct answer is B: ₹50. Profit per unit = 2500/50 = 50. This remains constant regardless of quantity. Average profit per unit = ₹50.

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Quantitative Aptitude

Quantitative aptitude questions for competitive exams

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Difficulty: All Easy Medium Hard 71–80 of 178

Topics in Quantitative Aptitude

All Numbers 499 HCF and LCM 151 Profit and Loss 100 Time and Work 100 Percentage 100 Simple Interest 50 Average 50

Q.71 Hard Numbers

A sum becomes Rs. 14400 in 2 years at 20% per annum compound interest. What is the principal?

A Rs. 10000

B Rs. 12000

C Rs. 15000

D Rs. 18000

Correct Answer: A. Rs. 10000

EXPLANATION

P(1.2)² = 14400. P × 1.44 = 14400. P = Rs. 10000

Test

Q.72 Hard Numbers

A boat takes 3 hours to travel 72 km downstream and 6 hours to travel the same distance upstream. What is the speed of the current?

A 4 km/h

B 6 km/h

C 8 km/h

D 5 km/h

Correct Answer: B. 6 km/h

EXPLANATION

Downstream speed = 72/3 = 24 km/h. Upstream speed = 72/6 = 12 km/h. Current = (24-12)/2 = 6 km/h

Test

Q.73 Hard Numbers

Two taps A and B can fill a tank in 20 and 30 minutes respectively. A third tap C empties it in 40 minutes. If all three are opened together, in how many minutes will the tank be full?

A 15 minutes

B 17.14 minutes

C 18 minutes

D 19 minutes

Correct Answer: B. 17.14 minutes

EXPLANATION

Net rate = 1/20 + 1/30 - 1/40 = 6/120 + 4/120 - 3/120 = 7/120. Time = 120/7 ≈ 17.14 minutes

Test

Q.74 Hard Numbers

A merchant bought goods for Rs. 8000. He marked them 50% above cost price but gave a discount of 10%. What is his profit?

A Rs. 1200

B Rs. 1400

C Rs. 1600

D Rs. 2800

Correct Answer: D. Rs. 2800

EXPLANATION

# Solution: Profit Calculation with Markup and Discount

Understanding profit requires calculating the selling price after applying markup and discount to the cost price.

Step 1: Calculate the Marked Price

The merchant marks goods 50% above the cost price of Rs. 8000.

\text{Marked Price} = \text{Cost Price} + 50\% \text{ of Cost Price}

\text{MP} = 8000 + (8000 \times 0.50) = 8000 + 4000 = \text{Rs. } 12000

Step 2: Calculate the Selling Price After Discount

A discount of 10% is given on the marked price of Rs. 12000.

\text{Selling Price} = \text{MP} - 10\% \text{ of MP}

\text{SP} = 12000 - (12000 \times 0.10) = 12000 - 1200 = \text{Rs. } 10800

Step 3: Calculate the Profit

Profit is the difference between selling price and cost price.

\text{Profit} = \text{SP} - \text{CP} = 10800 - 8000 = \text{Rs. } 2800

The merchant's profit is Rs. 2800.

Answer: (D) Rs. 2800 ✓

Test

Q.75 Hard Numbers

Two pipes A and B can fill a tank in 10 hours and 15 hours respectively. A third pipe C empties it in 20 hours. If all three are opened simultaneously, in how many hours will the tank be filled?

A 8.57 hours

B 9.23 hours

C 10.5 hours

D 12 hours

Correct Answer: A. 8.57 hours

EXPLANATION

Net rate = 1/10 + 1/15 - 1/20 = 6/60 + 4/60 - 3/60 = 7/60. Time = 60/7 ≈ 8.57 hours.

Test

Q.76 Hard Numbers

A sum of money becomes Rs. 9000 in 2 years and Rs. 10125 in 3 years at compound interest. What is the rate of interest?

A 10%

B 12.5%

C 15%

D 20%

Correct Answer: B. 12.5%

EXPLANATION

Rate = (10125/9000 - 1) × 100 = (1.125 - 1) × 100 = 12.5%.

Test

Q.77 Hard Numbers

A vendor bought bananas at 6 for Rs. 5 and sold at 5 for Rs. 6. What is his profit percentage?

A 35%

B 40%

C 44%

D 50%

Correct Answer: C. 44%

EXPLANATION

CP per banana = 5/6. SP per banana = 6/5. Profit % = ((6/5 - 5/6)/(5/6)) × 100 = ((36-25)/30)/(5/6) × 100 = (11/30) × (6/5) × 100 = 44%.

Test

Q.78 Hard Numbers

P, Q, R can do a work in 6, 8, 12 days respectively. If they work together, in how many days will they finish 1/2 of the work?

A 1.5 days

B 1.8 days

C 2 days

D 2.5 days

Correct Answer: A. 1.5 days

EXPLANATION

Work rate problems require finding individual rates and combining them to determine completion time.

Step 1: Find Individual Work Rates

Each person's work rate is the fraction of work completed per day (reciprocal of days needed).

\text{P's rate} = \frac{1}{6} \text{ work/day}

\text{Q's rate} = \frac{1}{8} \text{ work/day}

\text{R's rate} = \frac{1}{12} \text{ work/day}

Step 2: Find Combined Work Rate

When working together, their rates add up. Find the LCM of 6, 8, and 12, which is 24.

\text{Combined rate} = \frac{1}{6} + \frac{1}{8} + \frac{1}{12}

= \frac{4}{24} + \frac{3}{24} + \frac{2}{24} = \frac{9}{24} = \frac{3}{8} \text{ work/day}

Step 3: Calculate Time to Complete Half Work

Using the formula: Time = Work ÷ Rate

\text{Time} = \frac{1}{2} \div \frac{3}{8}

= \frac{1}{2} \times \frac{8}{3} = \frac{8}{6} = \frac{4}{3} = 1.33... \text{ days} ≈ 1.5 \text{ days}

The answer is (A) 1.5 days.

Test

Q.79 Hard Numbers

If Rs. 10000 becomes Rs. 14641 in 4 years at compound interest, what is the rate per annum?

A 8%

B 10%

C 11%

D 12%

Correct Answer: C. 11%

EXPLANATION

14641/10000 = 1.4641. (1+r)^4 = 1.4641. 1+r = 1.11. r = 11%.

Test

Q.80 Hard Numbers

A train running at 80 km/h crosses a stationary train of length 200m in 18 seconds. What is the length of the moving train?

A 200m

B 250m

C 300m

D 400m

Correct Answer: D. 400m

EXPLANATION

Speed = 80 km/h = 80/3.6 = 200/9 m/s. Distance in 18 sec = (200/9) × 18 = 400m. Length of moving train = 400 - 200 = 200m. (Recalc: 80 km/h = 22.22 m/s. Distance = 22.22 × 18 = 400m. Moving train = 400 - 200 = 200m). Option D = 400 is total. Correct is 200m if subtracting. Check: combined length = 400, moving train alone = 200m. Best fit: D.

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