Question

8 A and B can do a piece of work in 72 days. B and C can do it in 120 days. A and C can do it in 90 days. In what time can A alone do it?​

Answer 1

Step-by-step explanation:

60 days

According to question,

(A + B)’s one day’s work $latex = \frac{1}{72}&s=1$

(B + C)’s one day’s work $latex = \frac{1}{120}&s=1$

and (C + A)’s one day’s work $latex = \frac{1}{90}&s=1$

On adding all three,

2 (A + B + C)’s one day’s work $latex = \frac{1}{72}+ \frac{1}{120}+ \frac{1}{90}&s=1$

$latex = \frac{5+3+4}{360} = \frac{1}{30}&s=1$

∴ (A + B + C)’s one day’s work $latex = \frac{1}{60}&s=1$

∴ A, B and C together can finish the whole work in 60 days.

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

A and B can do a piece of work in 72 days.

$\rm\implies \: {(A + B)'}^{s} \: 1 \: day \: work \: = \: \dfrac{1}{72} - - - (1)$

Further given that,

B and C can do it in 120 days.

$\rm\implies \: {(B + C)'}^{s} \: 1 \: day \: work \: = \: \dfrac{1}{120} - - - (2)$

Also, given that

A and C can do it in 90 days.

$\rm\implies \: {(A + C)'}^{s} \: 1 \: day \: work \: = \: \dfrac{1}{90} - - - (3)$

On adding equation (1), (2) and (3), we get

$\rm \: \: 2{(A +B + C)'}^{s} \: 1 \: day \: work \: = \: \dfrac{1}{72} + \dfrac{1}{120} + \dfrac{1}{90}$

$\rm \: \: 2{(A +B + C)'}^{s} \: 1 \: day \: work \: = \: \dfrac{5 + 3 + 4}{360}$

$\rm \: \: 2{(A +B + C)'}^{s} \: 1 \: day \: work \: = \: \dfrac{12}{360}$

$\rm \: \: 2{(A +B + C)'}^{s} \: 1 \: day \: work \: = \: \dfrac{1}{30}$

$\rm\implies \: {(A +B + C)'}^{s} \: 1 \: day \: work \: = \: \dfrac{1}{60} - - - (4)$

On Subtracting equation (2) from equation (4), we get

$\rm \: {A'}^{s} \: 1 \: day \: work \: = \: \dfrac{1}{60} - \dfrac{1}{120}$

$\rm \: {A'}^{s} \: 1 \: day \: work \: = \: \dfrac{2 - 1}{120}$

$\rm \: {A'}^{s} \: 1 \: day \: work \: = \: \dfrac{1}{120}$

$\rm\implies \:A \: can \: alone \: finish \: the \: work \: in \: 120 \: days.$