Question

# Three persons A, B and C together can do a piece of work in 36 days. A and B together can do five times as much work as C alone; B and C together can do as much work as A alone. If A and C together can do n times as much work as B alone, then what is the value of n?

Answer

Considering in ratio form,

$$\frac{a+b}{c}= \frac{5}{1}$$

So, (a+b) = 5t and c = t ——–(i)

a + b + c =6t

$$\frac{b+c}{a}=\frac{1}{1}$$

So, (b+c) = t and a = t,

a + b + c = 2t (but total work done should be equal)

a + b + c = 2t x 3=6t

(b+c) = 3t and a = 3t ——–(ii)

On solving equations (i) & (ii), we have,

a=3t, c=t, b=2a

Now,

$$\frac{a+c}{b}=\frac{n}{1}$$

$$\frac{3t+t}{2t}=n$$

n=2

Answer (B) – 2