What are some CAT Chain Rule Practice Questions?
Study the given table carefully and answer the questions that follow :
Q1. A canteen requires 105 kgs of wheat for a week. How many kgs of wheat will it require for 58 days?
Answer: The canteen will require 870 kgs.
Solution: Daily requirement of wheat = Weekly requirement of wheat / Number of days in a week
Daily requirement of wheat = 105 kgs / 7 days
Daily requirement of wheat = 15 kgs
Find the requirement of wheat for 58 days.
Requirement of wheat for 58 days = Daily requirement of wheat × Number of days
Requirement of wheat for 58 days = 15 kgs × 58 days
Requirement of wheat for 58 days = 870 kgs
Therefore, the canteen will require 870 kgs of wheat for 58 days.
Q2. If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it?
Answer: 15 men will do the same piece of work in 60 hours.
Solution: Let the total work be represented by 1 unit.
Since 36 men can complete the work in 25 hours, the amount of work done by 36 men in 1 hour is 1/25 units.
The amount of work done by 15 men in 1 hour is proportional to the number of men working. Therefore, the amount of work done by 15 men in 1 hour = (15/36) × (1/25) = 1/60 units.
To find the time required for 15 men to complete 1 unit of work, we need to divide 1 unit by the amount of work done by 15 men in 1 hour.
Time required = 1 unit / (1/60 units per hour) = 60 hours.
Therefore, 15 men will do the same piece of work in 60 hours.
Q3. 35 women can do a piece of work in 15 days. How many women would be required to do the same work in 25 days?
Answer: 21 women would be required to do the same work in 25 days.
Solution: Let the total work be represented by 1 unit.
The amount of work done by 35 women in 1 day = 1/15 units.
The amount of work that needs to be done in 1 day to complete the work in 25 days = 1/25 units.
The number of women required to do 1/25 units of work in 1 day = (1/25 units) / (1/15 units) = (1/25) × (15/1) = 21 women.
Therefore, 21 women would be required to do the same work in 25 days.
Q4. A certain number of people were supposed to complete a work in 24 days. The work, however, took 32 days since 9 people were absent throughout. How many people were supposed to be working originally?
Answer: 36 people were supposed to be working originally to complete the work in 24 days.
Solution: Let the total work be represented by 1 unit.
The amount of work to be done in 1 day to complete the work in 24 days = 1/24 units.
The amount of work done in 1 day with the reduced number of workers = 1/32 units.
The ratio of the amount of work done with the reduced number of workers to the amount of work that should have been done = (1/32 units) / (1/24 units) = (1/32) × (24/1) = 3/4
If the number of people actually working is (3/4) × Original number of people, then:
(Original number of people - 9) = (3/4) × Original number of people
Original number of people = 36 people
Therefore, 36 people were supposed to be working originally to complete the work in 24 days.
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Q5. If 5 students utilize 18 pencils in 9 days, how long, at the same rate, will 66 pencils last for 15 students?
Answer: 66 pencils will last for 15 students for 11 days at the same rate.
Solution: Let the rate of pencil utilization be constant.
If 5 students utilize 18 pencils in 9 days, then the rate of pencil utilization per day per student = (18 pencils) / (5 students × 9 days) = 0.4 pencils.
The rate of pencil utilization per day for 15 students = 15 students × 0.4 pencils = 6 pencils.
The time (in days) for which 66 pencils will last for 15 students = Total number of pencils / Rate of pencil utilization per day for 15 students
= 66 pencils / 6 pencils per day
= 11 days
Therefore, 66 pencils will last for 15 students for 11 days at the same rate.
Q6. If 20 men can build a wall 56 metres long in 6 days, what length of a similar wall can be built by 35 men in 3 days?
Answer: 35 men can build a wall of 49 meters in 3 days.
Solution: Let the amount of work done be directly proportional to the length of the wall.
If 20 men can build a wall of 56 meters in 6 days, then the amount of work done by 20 men in 1 day = 56 meters / 6 days = 9.33 meters.
The amount of work that can be done by 35 men in 1 day = (35/20) × 9.33 meters = 16.33 meters.
The length of the wall that can be built by 35 men in 3 days = Amount of work that can be done by 35 men in 1 day × 3 days
= 16.33 meters × 3 days = 49 meters
Therefore, 35 men can build a wall of 49 meters in 3 days.
Q7. 8 men working for 9 hours a day complete a piece of work in 20 days. In how many days can 7 men working for 10 hours a day complete the same piece of work?
Answer: 7 men working for 10 hours a day can complete the same piece of work in 21 days.
Solution: Let the total amount of work be represented by 1 unit.
The amount of work done by 8 men in 1 day (9 hours) = 1 unit / 20 days = 0.05 units.
The amount of work done by 8 men in 1 hour = 0.05 units / 9 hours = 0.00556 units.
The amount of work done by 7 men in 1 hour = (7/8) × 0.00556 units = 0.00486 units.
The amount of work done by 7 men in 10 hours = 0.00486 units × 10 hours = 0.0486 units.
The number of days required for 7 men working for 10 hours a day to complete 1 unit of work = 1 unit / 0.0486 units per day = 20.58 days ≈ 21 days.
Therefore, 7 men working for 10 hours a day can complete the same piece of work in 21 days.
Q8. If 12 men or 18 women can do a work in 14 days, then in how many days will 8 men and 16 women do the same work?
Answer: Therefore, 8 men and 16 women can do the same work in 9 days.
Solution: Let the total amount of work be represented by 1 unit.
The amount of work done by 12 men or 18 women in 1 day = 1 unit / 14 days = 0.07143 units.
The amount of work done by 8 men in 1 day = (8/12) × 0.07143 units = 0.04762 units.
The amount of work done by 16 women in 1 day = (16/18) × 0.07143 units = 0.06349 units.
The total amount of work done by 8 men and 16 women in 1 day = 0.04762 units + 0.06349 units = 0.11111 units.
The number of days required for 8 men and 16 women to complete 1 unit of work = 1 unit / 0.11111 units per day = 9 days.
Therefore, 8 men and 16 women can do the same work in 9 days.
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Q9. Rocky can walk a certain distance in 40 days when he rests 9 hours a day. How long will he take to walk twice the distance, twice as fast and rest twice as long each day?
Answer: Rocky will take 400 days to walk twice the distance, twice as fast, and rest twice as long each day.
Solution: Let the original distance be represented by 1 unit.
The effective working time per day for the original scenario = 24 hours - 9 hours = 15 hours.
The new effective working time per day = 24 hours - (2 × 9 hours) = 6 hours.
The ratio of working times = 6 hours / 15 hours = 2/5.
The new distance = 2 × Original distance, so the ratio of distances = 2.
The time required for the new scenario = (Original time × Ratio of distances) / Ratio of working times
= (40 days × 2) / (2/5) = 400 days
Therefore, Rocky will take 400 days to walk twice the distance, twice as fast, and rest twice as long each day.
Q 10. If 9 engines consume 24 metric tonnes of coal, when each is working 8 hours a day; how much coal will be required for 8 engines, each running 13 hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type ?
Answer: 26 metric tons of coal will be required for 8 engines, each running 13 hours a day, given that 3 engines of the former type consume as much as 4 engines of the latter type.
Solution: Let the coal consumption per engine per hour for the former type be represented by x.
Coal consumption for 9 engines (former type) working for 8 hours = 9x × 8 = 24 metric tons
x = 24 / (9 × 8) = 0.3333 metric tons
Coal consumption per engine per hour (latter type) = (Coal consumption per engine per hour (former type) × 3) / 4
= (0.3333 × 3) / 4 = 0.25 metric tons
Coal consumption for 8 engines (latter type) running for 13 hours = 8 × 0.25 × 13 = 26 metric tons
Therefore, 26 metric tons of coal will be required for 8 engines, each running 13 hours a day, given that 3 engines of the former type consume as much as 4 engines of the latter type.
Q 11. A garrison of 3300 men had provisions for 32 days, when given at the rate of 850 gms per head. At the end of 7 days, a reinforcement arrives and it was found that the provisions will last 17 days more, when given at the rate of 825 gms per head. What is the strength of the reinforcement?
Answer: the strength of the reinforcement is 1700 men.
Solution: Let the total provisions for 3300 men be represented by x grams.
x = 3300 × 850 grams × 32 days = 89,280,000 grams
Provisions consumed by 3300 men in 7 days = 3300 × 850 grams × 7 days = 19,635,000 grams
Remaining provisions after 7 days = x - 19,635,000 grams = 69,645,000 grams
Total number of men = Remaining provisions after 7 days / (825 grams × 17 days)
= 69,645,000 grams / (825 grams × 17 days) = 5000 men
Strength of the reinforcement = Total number of men - Initial garrison
= 5000 men - 3300 men = 1700 men
Therefore, the strength of the reinforcement is 1700 men.
Q 12. Two coal loading machines each working 12 hours per day for 8 days handle 9000 tonnes of coal with an efficiency of 90% while 3 other coal loading machines at an efficiency of 80% are set to handle 12000 tonnes of coal in 6 days. Find how many hours per day each should work.
Answer: each of the three coal loading machines should work for 16 hours per day to handle 12000 tonnes of coal in 6 days with an efficiency of 80%.
Solution: Let the rate of coal handling per hour with 100% efficiency be represented by x tonnes per hour.
For the two machines handling 9000 tonnes with 90% efficiency:
9000 tonnes = 0.9 × x × (2 × 12 × 8) hours
x = 52.0833 tonnes per hour
For the three machines handling 12000 tonnes with 80% efficiency in 6 days:
12000 tonnes = 0.8 × x × (3 × y × 6) hours
y = 12000 tonnes / (0.8 × 52.0833 tonnes per hour × 3 × 6 days) = 16 hours per day
Therefore, each of the three coal loading machines should work for 16 hours per day to handle 12000 tonnes of coal in 6 days with an efficiency of 80%.
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Q13. If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?
Answer: the cost of y meters of wire at the same rate is (d / x) × y rupees.
Solution: Let the cost per meter of wire be represented by r rupees.
The cost of x meters of wire = r × x = d rupees
r = d / x
The cost of y meters of wire = Cost per meter of wire × Length of wire (y)
= (d / x) × y rupees
Therefore, the cost of y meters of wire at the same rate is (d / x) × y rupees.
Q14. The price of 5.5 dozen pens is ` 1287. What is the price of 16 such pens?
Answer: the price of 16 pens is ₹ 312.
Solution: Let the cost of 1 pen be represented by x rupees.
The cost of 66 pens = 66x = ₹ 1287
x = ₹ 1287 / 66 = ₹ 19.5
The cost of 16 pens = 16x = 16 × ₹ 19.5 = ₹ 312
Therefore, the price of 16 pens is ₹ 312.
Q15. If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?
Answer: 200 grams of potatoes will cost 48 paise.
Solution: Let the cost of 1 gram of potatoes be represented by x paise.
The cost of 250 grams (1/4 kg) of potatoes = 250x = 60 paise
x = 60 / 250 = 0.24 paise
The cost of 200 grams of potatoes = 200x = 200 × 0.24 = 48 paise
Therefore, 200 grams of potatoes will cost 48 paise.
Q16. If 11.25 m of a uniform iron rod weighs 42.75 kg, what will be the weight of 6 m of the same rod?
Answer: the weight of 6 meters of the same iron rod will be 22.8 kilograms.
Solution: Let the weight of 1 meter of the iron rod be represented by x kilograms.
The weight of 11.25 meters of the rod = 11.25x = 42.75 kg
x = 42.75 kg / 11.25 m = 3.8 kg/m
The weight of 6 meters of the rod = 6x = 6 × 3.8 kg/m = 22.8 kg
Therefore, the weight of 6 meters of the same iron rod will be 22.8 kilograms.
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