Question

A started a work and left after working for 2 days. Then B was called and he finished the work in 9 days. Had A left the work after working for 3 days, B would have finished the remaining work in 6 days. In how many days can each of them, working alone finish the whole work ? 

(a) 5 days, 8.5 days 

(b) 2.5 days, 7.5 days 

(c) 5 days, 15 days 

(d) 3 days, 15 days

Answer 1

(c) 5 days, 15 days

Suppose A and B do the work in x and y days respectively.

Now, work done by A in 2 days + work done by B in 9 days = 1

\(\Rightarrow\) \(\frac{2}{X}+\frac{9}{y}\) = 1

Similarly, \(\frac{3}{X}+\frac{6}{y}\) = 1

Let \(\frac{1}{X}\) = a and \(\frac{1}{y}\) = b . then the equations become

2a + 9b = 1  ...................(i)

3a + 6b = 1 .....................(ii)

Performing (i) × 2 – (ii) × 3, we get 

(6a + 12b) – (6a + 27b) = 2 – 3

\(\Rightarrow\) – 15b = –1  \(\Rightarrow\) b = \(\frac{1}{15}\) \(\Rightarrow\) x = 15

\(\therefore\) Putting the value of b in (i)

2a + 9 × \(\frac{1}{15}\) = 1

\(\Rightarrow\) 2a = 1 - \(\frac{3}{5}\) = \(\frac{2}{5}\)

\(\Rightarrow\) a = \(\frac{1}{5}\)  \(\Rightarrow\) y = 5