Question

Raju can do a piece of work in 10 days, Vicky in 12 days and Tinku in 15 days. They all start
the work together, but Raju leaves after 2 days and Vicky leaves 3 days before the work is completed. In how many days is the work completed?
(1) 5 days
(2) 16 days
(3) 7 days
(4) 8 days

Answer 1

Step by step solution

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One day's work of Raju = 1/0

" " " " Vicky = 1/12

" " " " Tinku = 1/15

2 day's work of all = 2 x ( 1/10 + 1/12 + 1/15 ) ------------------- ( 2 days)

= 2x 15/60

= 1/2

Remaining work = 1 - 1/2 = 1/2

Last 3 day's work is done by Tinku alone as Vicky leaves 3 days before the work is completed.

So, Tinku's 3 day's work = 3 x 1/15 = 1/5 ....................................... ( 3 days)

Total work done so far, 1/2 + 1/5 = 7/10

Remaining work = 1 - 7/10 = 3/10

This 3/10 work is done by both, Vicky and Tinku

one day's work of Vicky and Tinku = 1/12 + 1/15 = 9/60 = 3/20

Now , we will use Unitary Method to find the number of days taken by Vicky and Tinku to complete the remaining 3/10 of work.

Vicky + Tinku complete 3/20 part in = 1 day

" " " 1 part  = 1 x 3/20

" " " 3/10 part = 3/20 ÷ 3/10

= 3/20 x 10/3

= 1/2

So, Vicky + Tinku complete 3/10 remaining part in 2 days ................( 2 days)

Total days taken to complete the work are 2 + 3 + 2 + = 7 days.

so, the required answer is 7 days.

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