Question

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 ?​

Answer 1

$\huge\underline\bold {Answer:}$

(A + B)’s one days’ work = 1/30

(B + C)’s one days’ work = 1/24 .....(1)

(C + A)’s one days’ work = 1/20

Therefore (A + B + C)’s one days’ work

$\frac{1}{2} ( \frac{1}{30} + \frac{1}{24} + \frac{1}{20} ) \\ = \frac{1}{2} \times ( \frac{20 + 25 + 30}{600} ) \\ = \frac{75}{1200} \\ = \frac{1}{16} \: \: \: \: \: \: \: ...(2)$

(A + B + C)’s 10 days’ work

= 10/6 = 5/8

From (1) and (2), A's one days’ work

= 1/16 – 24

= 1/48

Therefore remaining 3/8 of the work is done by A alone in 3/8 × 48

= 18 days.

Answer 2

$\blue{ <strong><u>Given</u></strong><strong><u>:</u></strong><strong><u>-</u></strong> }$

• 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.

$\red{ <strong><u>To</u></strong><strong><u> </u></strong><strong><u>\</u></strong><strong><u>:</u></strong><strong><u> </u></strong><strong><u>find</u></strong><strong><u>:</u></strong><strong><u>-</u></strong> }$

• How many days more will A take to finish the work ?

$\green{Solution:-}$

• (A + B)’s one days’ work = 1/30

• (B + C)’s one days’ work = 1/24 .....(1)

• (C + A)’s one days’ work = 1/20

Therefore (A + B + C)’s one days’ work

$\begin{gathered}\frac{1}{2} ( \frac{1}{30} + \frac{1}{24} + \frac{1}{20} ) \\ = \frac{1}{2} \times ( \frac{20 + 25 + 30}{600} ) \\ = \frac{75}{1200} \\ = \frac{1}{16} \: \: \: \: \: \: \: ...(2)\end{gathered}$

• (A + B + C)’s 10 days’ work

= 10/6 = 5/8

From (1) and (2), A's one days’ work

= 1/16 – 24

= 1/48

Therefore remaining 3/8 of the work is done by A alone in 3/8 × 48

= 18 days.

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