Time and Work Practice Test 3 with solutions

Question : 9 of 40

Marks: +1, -0

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?

36 days
30 days
24 days
18 days

Validate

Solution:

2 (A + B + C)'s 1 day's work =

1/{30}+1/{24}+1/{20}

{15}/{120}

1/8

Hence, (A + B + C)'s 1 day's work =

1/{16}

Now, A's 1 day's work =

1/{16}-1/{24}

1/{48}

Again, (A + B + C)'s 10 days' work = 10 ×

1/{16}

5/8

Remaining part of work = 1 –

5/8

3/8

, which will be done by A alone.
Hence, time taken by A to complete the remaining work =

{3/8}/{1/{48}}

3/8 × 48

= 18 days.

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