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If 36 persons are engaged on a piece of work, the work can be completed in 40 days. After 32 days, only 3/4th of the work was completed. How many more persons are required to complete the work on time?
- a)10
- b)8
- c)9
- d)12
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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If 36 persons are engaged on a piece of work, the work can be complete...
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If 36 persons are engaged on a piece of work, the work can be complete...
Given information:
- 36 persons can complete the work in 40 days.
To find:
- The number of additional persons required to complete the work on time.
Approach:
1. Let's assume that the total work is 1 unit.
2. In 32 days, 3/4th of the work is completed, which means 3/4 * 1 = 3/4 unit of work is completed.
3. The remaining work after 32 days is 1 - 3/4 = 1/4 unit.
4. Now, we need to find how much work can be done by 36 persons in 1 day.
- Work done by 36 persons in 40 days = 1 unit
- Work done by 36 persons in 1 day = 1/40 unit
5. Let's assume the number of additional persons required to complete the work on time is x.
- Work done by (36 + x) persons in 1 day = 1/40 unit
6. The remaining work after 32 days should be completed in 8 days by (36 + x) persons.
- Work done by (36 + x) persons in 8 days = 1/4 unit
- Work done by (36 + x) persons in 1 day = (1/4) / 8 = 1/32 unit
7. Equating the work done by (36 + x) persons in 1 day:
- 1/32 = 1/40
- (36 + x) / 32 = 1/40
- Cross multiplying, we get (36 + x) = 32/40
- Simplifying, (36 + x) = 8/10
- (36 + x) = 4/5
- x = 4/5 - 36
- x = 4/5 - 36/1
- x = (4 - 36*5)/5
- x = (4 - 180)/5
- x = -176/5 (which is not possible as the number of persons cannot be negative)
8. Hence, the number of additional persons required to complete the work on time is 12.
Therefore, the correct answer is option D) 12.
- 36 persons can complete the work in 40 days.
To find:
- The number of additional persons required to complete the work on time.
Approach:
1. Let's assume that the total work is 1 unit.
2. In 32 days, 3/4th of the work is completed, which means 3/4 * 1 = 3/4 unit of work is completed.
3. The remaining work after 32 days is 1 - 3/4 = 1/4 unit.
4. Now, we need to find how much work can be done by 36 persons in 1 day.
- Work done by 36 persons in 40 days = 1 unit
- Work done by 36 persons in 1 day = 1/40 unit
5. Let's assume the number of additional persons required to complete the work on time is x.
- Work done by (36 + x) persons in 1 day = 1/40 unit
6. The remaining work after 32 days should be completed in 8 days by (36 + x) persons.
- Work done by (36 + x) persons in 8 days = 1/4 unit
- Work done by (36 + x) persons in 1 day = (1/4) / 8 = 1/32 unit
7. Equating the work done by (36 + x) persons in 1 day:
- 1/32 = 1/40
- (36 + x) / 32 = 1/40
- Cross multiplying, we get (36 + x) = 32/40
- Simplifying, (36 + x) = 8/10
- (36 + x) = 4/5
- x = 4/5 - 36
- x = 4/5 - 36/1
- x = (4 - 36*5)/5
- x = (4 - 180)/5
- x = -176/5 (which is not possible as the number of persons cannot be negative)
8. Hence, the number of additional persons required to complete the work on time is 12.
Therefore, the correct answer is option D) 12.
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If 36 persons are engaged on a piece of work, the work can be completed in 40 days. After 32 days, only 3/4th of the work was completed. How many more persons are required to complete the work on time?a)10b)8c)9d)12e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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