Time & Work

Some machines complete the work in 4 days. But if 4 other machines are included in this work, then the job shall be completed in 2 days. If capacities of all machines are same, then in how many days 2 machines can complete this work ?

** Option:**

**A.**6 days

**B.**8 days

**C.**10 days

**D.**12 days

**Answer: B . 8 days**

** Justification:**

Suppose, originally there are x machines.

x machines 1 days work = $ 1/4 $ or 1 machine's 1 day's work $1/{4x}$ .... (i)

Also (x + 4) machines 1 days's work = $1/2$

1 machine's 1 day's work = $ 1/ {2(x + 4)} $... (ii)

Equating (i) and (ii),

$ 1/{4x} = 1/ {2(x + 4)} $ or 2x + 8 = 4x

or 2x = 8

or x = 4

Now, 1 machine's 1 days work = $ 1/{4x4} = 1/16$

2 machine's 1 day's work = $2/16 = 1/8 $

Hence, 2 machines can finish the work in 8 days.