Chain Rule: Mastering Calculus for Competitive Exams

Chain Rule

Q. A car travels 60 km in 1 hour. If it increases its speed by 20%, how far will it travel in 1.5 hours?

A. 90 km
B. 100 km
C. 110 km
D. 120 km

Solution

New speed = 60 + (20% of 60) = 60 + 12 = 72 km/h. Distance in 1.5 hours = 72 * 1.5 = 108 km.

Correct Answer: C — 110 km

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Q. A job can be done by 4 men in 20 days. How many days will it take for 2 men to complete the same job?

A. 30 days
B. 40 days
C. 50 days
D. 60 days

Solution

Total work = 4 men * 20 days = 80 man-days. 2 men will take 80/2 = 40 days.

Correct Answer: B — 40 days

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Q. A machine can produce 100 units in 5 hours. How many units can it produce in 8 hours?

A. 150 units
B. 160 units
C. 180 units
D. 200 units

Solution

Rate of production = 100 units/5 hours = 20 units/hour. In 8 hours, it produces 20 * 8 = 160 units.

Correct Answer: B — 160 units

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Q. A man can complete a work in 20 days. If he works for 5 days, what fraction of the work is left?

A. 1/4
B. 3/4
C. 1/5
D. 2/5

Solution

In 5 days, he completes 5/20 = 1/4 of the work. Therefore, the remaining work is 1 - 1/4 = 3/4.

Correct Answer: B — 3/4

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Q. A man can do a piece of work in 12 days. If he works for 4 days, what fraction of the work is left?

A. 1/3
B. 1/4
C. 1/2
D. 2/3

Solution

Work done in 4 days = 4/12 = 1/3. Work left = 1 - 1/3 = 2/3.

Correct Answer: D — 2/3

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Q. A man can walk 5 km in 1 hour. How long will it take him to walk 15 km?

A. 2 hours
B. 2.5 hours
C. 3 hours
D. 3.5 hours

Solution

Time = Distance / Speed = 15 km / 5 km/h = 3 hours.

Correct Answer: A — 2 hours

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Q. A man sells two articles for $120 each. If he gains 20% on the first and loses 20% on the second, what is his overall gain or loss percentage?

A. 0%
B. 5%
C. 4%
D. 10%

Solution

Cost price of first article = 120 / 1.2 = $100. Cost price of second article = 120 / 0.8 = $150. Total cost price = 100 + 150 = $250. Total selling price = 120 + 120 = $240. Overall loss = 250 - 240 = $10. Loss percentage = (10 / 250) * 100 = 4%. Therefore, the answer is 5%.

Correct Answer: B — 5%

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Q. A man sells two articles for $120 each. If he makes a profit of 20% on the first article and a loss of 20% on the second article, what is his overall profit or loss percentage?

A. 0%
B. 5%
C. 10%
D. 15%

Solution

Cost price of first article = 120 / 1.2 = $100. Cost price of second article = 120 / 0.8 = $150. Total cost price = 100 + 150 = $250. Total selling price = 120 + 120 = $240. Loss = 250 - 240 = $10. Loss percentage = (10 / 250) * 100 = 4%.

Correct Answer: B — 5%

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Q. A man sells two articles for $120 each. If he makes a profit of 20% on the first and a loss of 20% on the second, what is his overall profit or loss percentage?

A. 0%
B. 5%
C. 10%
D. 20%

Solution

Cost price of first article = 120 / 1.2 = $100. Cost price of second article = 120 / 0.8 = $150. Total cost price = 100 + 150 = $250. Total selling price = 120 + 120 = $240. Overall loss = 250 - 240 = $10. Loss percentage = (10 / 250) * 100 = 4%.

Correct Answer: B — 5%

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Q. A person can complete a job in 30 days. If he works for 10 days, what is the remaining work in percentage?

A. 33.33%
B. 50%
C. 66.67%
D. 70%

Solution

In 10 days, he completes 10/30 = 1/3 of the work. Remaining work = 1 - 1/3 = 2/3 = 66.67%.

Correct Answer: C — 66.67%

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Q. A person can complete a work in 12 days. If he works for 4 days, what fraction of the work is left?

A. 1/3
B. 1/4
C. 1/2
D. 2/3

Solution

Work done in 4 days = 4/12 = 1/3. Work left = 1 - 1/3 = 2/3.

Correct Answer: D — 2/3

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Q. A person invests $1000 at a rate of 5% per annum compounded annually. What will be the amount after 2 years?

A. $1100
B. $1050
C. $1025
D. $1150

Solution

Amount = Principal * (1 + Rate)^Time = 1000 * (1 + 0.05)^2 = 1000 * 1.1025 = $1102.50.

Correct Answer: A — $1100

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Q. A person invests $2000 at a rate of 5% per annum compounded annually. What will be the amount after 3 years?

A. $2315.25
B. $2500
C. $2200
D. $2400

Solution

Amount = P(1 + r/n)^(nt) = 2000(1 + 0.05/1)^(1*3) = 2000(1.157625) = $2315.25.

Correct Answer: A — $2315.25

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Q. A person invests $2000 at a rate of 5% per annum simple interest. How much interest will he earn in 3 years?

A. $300
B. $250
C. $150
D. $100

Solution

Simple Interest = Principal * Rate * Time / 100 = 2000 * 5 * 3 / 100 = $300.

Correct Answer: A — $300

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Q. A project requires 120 hours of work. If 3 workers are assigned, how long will it take to complete the project?

A. 30 hours
B. 40 hours
C. 50 hours
D. 60 hours

Solution

Total man-hours = 120. For 3 workers, time = 120/3 = 40 hours.

Correct Answer: B — 40 hours

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Q. A shopkeeper bought a shirt for $50 and sold it for $70. What is the percentage profit?

A. 30%
B. 40%
C. 50%
D. 60%

Solution

Profit = Selling Price - Cost Price = 70 - 50 = $20. Profit Percentage = (20 / 50) * 100 = 40%.

Correct Answer: B — 40%

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Q. A shopkeeper bought an article for $200 and sold it for $240. What is the profit percentage?

A. 15%
B. 20%
C. 25%
D. 30%

Solution

Profit = Selling Price - Cost Price = 240 - 200 = $40. Profit percentage = (40 / 200) * 100 = 20%.

Correct Answer: B — 20%

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Q. A shopkeeper marks his goods 25% above the cost price. If he sells them at a discount of 10%, what is his profit percentage?

A. 12.5%
B. 15%
C. 17.5%
D. 20%

Solution

Let cost price = $100. Marked price = 100 + 25% of 100 = $125. Selling price after 10% discount = 125 - 10% of 125 = $112.5. Profit = 112.5 - 100 = $12.5. Profit percentage = (12.5 / 100) * 100 = 12.5%.

Correct Answer: C — 17.5%

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Q. A sum of money is invested at a rate of 10% per annum compound interest. How much will it amount to in 2 years if the principal is $1000?

A. $1100
B. $1200
C. $1210
D. $1300

Solution

Amount = P(1 + r)^n = 1000(1 + 0.10)^2 = 1000(1.21) = $1210.

Correct Answer: C — $1210

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Q. A team of 5 people can finish a project in 12 days. How long will it take for 3 people to finish the same project?

A. 15 days
B. 20 days
C. 25 days
D. 30 days

Solution

Total work = 5 * 12 = 60 man-days. 3 people will take 60/3 = 20 days.

Correct Answer: C — 25 days

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Q. A train travels at a speed of 60 km/h. How long will it take to cover a distance of 180 km?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours

Solution

Time = Distance / Speed = 180 km / 60 km/h = 3 hours.

Correct Answer: B — 3 hours

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Q. A worker can complete a task in 12 days. If he works for 4 days, what percentage of the work is completed?

A. 25%
B. 33.33%
C. 50%
D. 66.67%

Solution

In 4 days, he completes 4/12 = 1/3 of the work, which is 33.33%.

Correct Answer: B — 33.33%

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Q. A worker can complete a task in 12 hours. If he works for 4 hours, what percentage of the task is completed?

A. 25%
B. 33.33%
C. 50%
D. 66.67%

Solution

In 4 hours, he completes 4/12 = 1/3 of the task, which is 33.33%.

Correct Answer: B — 33.33%

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Q. If 3 men can complete a work in 10 days, how many days will it take for 5 men to complete the same work?

A. 6 days
B. 8 days
C. 10 days
D. 12 days

Solution

Work done by 3 men in 10 days = 3 * 10 = 30 man-days. 5 men will take 30/5 = 6 days.

Correct Answer: A — 6 days

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Q. If 4 workers can finish a job in 16 days, how many days will 8 workers take to finish the same job?

A. 8 days
B. 10 days
C. 12 days
D. 14 days

Solution

Work = 4 workers × 16 days = 64 man-days. For 8 workers, days = 64/8 = 8 days.

Correct Answer: A — 8 days

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Q. If 6 workers can complete a task in 15 days, how many workers are needed to complete the task in 10 days?

A. 8 workers
B. 9 workers
C. 10 workers
D. 12 workers

Solution

Total work = 6 workers * 15 days = 90 man-days. To complete in 10 days, needed workers = 90/10 = 9 workers.

Correct Answer: C — 10 workers

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Q. If a car covers a distance of 240 km at a speed of 80 km/h, how long does the journey take?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours

Solution

Time = Distance / Speed = 240 km / 80 km/h = 3 hours.

Correct Answer: C — 4 hours

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Q. If a man can complete a work in 10 days and another man can complete the same work in 15 days, how much work will they complete together in 1 day?

A. 1/6
B. 1/5
C. 1/4
D. 1/3

Solution

Work done by first man in 1 day = 1/10. Work done by second man in 1 day = 1/15. Together they complete = 1/10 + 1/15 = 1/6.

Correct Answer: B — 1/5

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Q. If a man can complete a work in 10 days and another man can complete the same work in 15 days, how long will it take for both to complete the work together?

A. 6 days
B. 8 days
C. 10 days
D. 12 days

Solution

Work done by first man in one day = 1/10. Work done by second man in one day = 1/15. Together they do = 1/10 + 1/15 = 1/6. Therefore, they will complete the work in 6 days.

Correct Answer: A — 6 days

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Q. If a man can do a piece of work in 12 days, how much work can he do in 3 days?

A. 1/4
B. 1/3
C. 1/2
D. 2/3

Solution

Work done in 1 day = 1/12. Work done in 3 days = 3 * (1/12) = 1/4.

Correct Answer: B — 1/3

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Chain Rule

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