Unitary Method problems
- 1. Nine examiners can examine a certain number of answer books in 12 days by working 5 hours a day. How many hours in a day should 4 examiners work to examine twice the number of answer books in 30 days?
Options- A. 9
- B. 11
- C. 13
- D. 17 Discuss
Correct Answer: 9
Explanation:
- 2. A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
Options- A. 39
- B. 37
- C. 42
- D. 56 Discuss
Correct Answer: 42
Explanation:
As per the given question ,
Food of 150 men for 45 days = 150 × 45 = 6750 unit
After 10 days , Food of 150 men for 150 × 10 = 1500 unit
And after 10 days remaining men = 150 - 25 = 125
and remaining food = 6750 - 1500 = 5250 unit
Let D be the number of days for which the remaining food .
So, 125 × D = 5250
? D = 5250 /125 = 42 days
- 3. Nine engines consume 24 metric tonnes of coal, when each is working 8 hours day. How much coal is required for 8 engines, each running 13 hours a day, if 3 engines of former type consume as much as 4 engines of latter type?
Options- A. 20 metric tonnes
- B. 39 metric tonnes
- C. 23 metric tonnes
- D. 26 metric tonnes Discuss
Correct Answer: 26 metric tonnes
Explanation:
Let required amount of coal be y metric tonnes
9 engines consumes 24 metric tonnes of coal in 8 hours a day.
More engines, more amount of coal (direct proportion)
If 3 engines of first type consume 1 unit, then 1 engine will consume 1/3 unit which is its the rate of consumption.
If 4 engines of second type consume 1 unit, then 1 engine will consume 1/4 unit which is its the rate of consumption
More rate of consumption, more amount of coal (direct proportion)
More hours, more amount of coal(direct proportion)
Now we have , 9 × ( 1 / 3 ) × 8 × y = 8 × ( 1 / 4 ) × 13 × 24
? 3 × 8 × y = 8 × 6 × 13
? 3 × y = 6 × 13 ? y = 2 x 13 = 26 metric tonnes
- 4. If 40 men can make 30 boxes in 20 days, How many more men are needed to make 60 boxes in 25 days?
Options- A. 20
- B. 24
- C. 27
- D. 28 Discuss
Correct Answer: 24
Explanation:
- 5. 2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the same in 11 days. Then, 8 men and 6 boys can do three times the amount of this work in.
Options- A. 18
- B. 21
- C. 34
- D. 39 Discuss
Correct Answer: 21
Explanation:
- 6. If 20 men can build a wall 56 meters long in 6 days , what length of a similar wall can be built by 35 men in 3 days?
Options- A. 40
- B. 43
- C. 48
- D. 49 Discuss
Correct Answer: 49
Explanation:
- 7. A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is:
Options- A. 4
- B. 9
- C. 14
- D. 7 Discuss
Correct Answer: 9
Explanation:
- 8. A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the begining and 100 more after 35 days and completes the work in stipulated time.
If he had not engaged the additional men, how many days behind schedule would it be finished?
Options- A. 7
- B. 18
- C. 12
- D. None Discuss
Correct Answer: None
Explanation:
- 9. 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
Options- A. 24
- B. 23
- C. 34
- D. 39 Discuss
Correct Answer: 24
Explanation:
- 10. Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in :
Options- A. 16
- B. 12
- C. 8
- D. 3 Discuss
Correct Answer: 3
Explanation:
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