


1.
If 15 toys cost Rs. 234, what do 35 toys cost?
2.
If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it?
3.
If the wages of 6 men for 15 days be Rs. 2100, then find the wages of 9 men for 12 days.
Answer & Solution
Answer: c) Rs. 2520
Solution: Let the required wages be Rs. x. More men, More wages. (Direct Proportion) Less days, Less wages. (Direct Proportion) Men 6 : 9 Days 15 : 12 :: 2100 : x (6 * 15 * x) = (9 * 12 * 2100) => x = [(9 * 12 * 2100) / (6 * 15)] = 2520. Hence, the required wages are Rs. 2520. 4.
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 & Solution
Answer: b) 49 m
Solution: Let the required length be x metres. More men, More length built. (Direct Proportion) Less days, Less length built. (Direct Proportion) Men 20 : 35 Days 6 : 3 :: 56 : x (20 * 6 * x) = (35 * 3 * 56) => x = [(35 * 3 * 56) / 120] = 49. Hence, the required length is 49 m. 5.
If 5 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day?
Answer & Solution
Answer: d) 15
Solution: Let the required number of days be x. More men, Less days. (Indirect Proportion). Less hours per day, More days. (Indirect Proportion) Men 18 : 15 Hours per days 8 : 9 :: 16 : x (18 * 8 * x = (15 * 9 * 16) => x = [(15 * 144) / 144 ] = 15. Hence, the required number of days = 15. 6.
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 & Solution
Answer: c) 26
Solution: Let 3 engines of former type consume 1 unit in 1 hour. Then, 4 engines of latter type consume 1 unit in 1 hour. 1 engine of former type consumes 1/3 unit in 1 hour. 1 engine of latter type consumes 1/4 unit in 1hour. Let the required consumption of coal be x units. Less engines, Less coal consumed. (Direct Proportion) More working hours, More coal consumed. (Direct Proportion). Less rate of consumption, Less coal consumed. (Direct Proportion). Number of engines 9 : 8 Working hours 8 : 13 Rate of consumption 1/3 : 1/4 :: 24 : x [9 * 8 * (1/3) * x] = [8 * 13 * (1/4) * 24] => 24x = 624 => x = 26. Hence, the required consumption of coal = 26 metric tonnes. 7.
A contract is to be cpmpleted in 46 days and 117 men were set to work, each working 8 hours a day. After 33 days, 4/7 of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day?
Answer & Solution
Answer: d) 81
Solution: Remaning work = [1  (4/7)] = 3/7. Remaining period = (46  33) days = 13 days. Let the total men working at it be x. Less work, Less men. (Direct Proportion) Less days, More men. (Indirect Proportion) More Hrs/Day, Less men. (Indirect Proportion). Work 4/7 : 3/7 Days 13 : 22 Hrs/Day 9 : 8 :: 117 : x (4/7) * 13 * 9 * x = (3/7) * 33 * 8 * 117 => x = [(3 * 33 * 8 * 117) / (4 * 13 * 9)] = 198. Additional men to be employed = (198  117) = 81. 