Quantitative Aptitude
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Question 41
A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
Correct Answer: Option A
2(A + B + C)'s 1 day's work
| = |  |
1 | + | 1 | + | 1 |  |
= | 15 | = | 1 | . |
| 30 | 24 | 20 | 120 | 8 |
Therefore, (A + B + C)'s 1 day's work
| = | 1 | = | 1 | . |
| 2 x 8 | 16 |
| Work done by A, B, C in 10 days = | 10 | = | 5 | . |
| 16 | 8 |
| Remaining work = | |
1 - | 5 | |
= | 3 | . |
| 8 | 8 |
| A's 1 day's work = | |
1 | - | 1 | |
= | 1 | . |
| 16 | 24 | 48 |
| Now, | 1 | work is done by A in 1 day. |
| 48 |
| So, | 3 | work will be done by A in | |
48 x | 3 | |
|
| 8 | 8 |
= 18 days.
Question 42
A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
Correct Answer: Option C
Let A's 1 day's work = x and B's 1 day's work = y.
| Then, x + y = | 1 | and 16x + 44y = 1. |
| 30 |
Solving these two equations, we get:
| x = | 1 | and y = | 1 |
| 60 | 60 |
 B's 1 day's work = |
1 | . |
| 60 |
Hence, B alone shall finish the whole work in 60 days.
Question 43
A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :
Correct Answer: Option C
| (A + B + C)'s 1 day's work = | 1 | ; |
| 6 |
| (A + B)'s 1 day's work = | 1 | ; |
| 8 |
| (B + C)'s 1 day's work = | 1 | . |
| 12 |
| (A + C)'s 1 day's work |
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So, A and C together will do the work in 8 days.
Question 44
X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?
Correct Answer: Option A
| Work done by X in 8 days = | |
1 | x 8 | |
= | 1 | . |
| 40 | 5 |
| Remaining work = | |
1 - | 1 | |
= | 4 | . |
| 5 | 5 |
| Now, | 4 | work is done by Y in 16 days. |
| 5 |
Whole work will be done by Y in:
|
16 x | 5 | |
= 20 days. | |
| 4 |
| X's 1 day's work = |
1 | , Y's 1 day's work = | 1 | . |
| 40 | 20 |
| (X + Y)'s 1 day's work = | |
1 | + | 1 | |
= | 3 | . |
| 40 | 20 | 40 |
Hence, X and Y will together complete the work in:
|
40 | |
= 13 | 1 | days. | |
| 3 | 3 |