Question

A and B together can do a piece of work in 12 days, which Band C together can do in
16 days. After A has been working at it for 5 days and B for 7 days, C finishes in 13 days. In how
many days C alone will do the work?
(A) 16
(B) 24
(C) 36
(D) 48
​

Answer 1

Answer:

36 days

Step-by-step explanation:

using linear equation its solved

Answer 2

Answer:

Correct option is (B) 24

Step-by-step explanation:

A and B together can do a piece of work in 12 days.

∴ A and B together each day can complete $\frac{1}{12}$ part of the work.

Similarly, B and C together each day can complete $\frac{1}{16}$ part of the work

Let's assume A can do it in x days, i.e. in each day A can complete $\frac{1}{x}$ part

Let's also assume B can do it in y days.  In each day B can complete $\frac{1}{y}$ part

Let's also assume C can do it in z days.  In each day C can complete $\frac{1}{z}$ part

According to the problem:

$\frac{1}{x} + \frac{1}{y} = \frac{1}{12}$

and $\frac{1}{y} + \frac{1}{z} = \frac{1}{16}$

and [1 - ($\frac{5}{x}$ + $\frac{7}{y}$)] = $\frac{13}{z}$

=> 1 - 5($\frac{1}{x} + \frac{1}{y}$) - $\frac{2}{y}$ - $\frac{2}{z}$ = $\frac{11}{z}$

=> 1 - $\frac{5}{12}$ - $\frac{2}{16}$ = $\frac{11}{z}$

=> $\frac{48 - 20 -6}{48}$ = $\frac{11}{z}$

=>$\frac{22}{48}$ = $\frac{11}{z}$

∴ z = 24

∴ Correct option is (B) 24