Arithmetic -2 (GATE-2010)

5 skilled workers can build a wall in 20days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30 days; If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall?

(A) 20 days

(B) 18 days

(C) 16 days

(D) 15 days
Solution follows here:

Solution:

5 skilled workers can build a wall in 20days

=> 1 skilled worker can build a wall in 20 * 5 = 100 days

=> 1 skilled worker can complete 1/100 th of work in one day

8 semi-skilled workers can build a wall in 25days

=> 1 semi-skilled worker can build a wall in 25 * 8 = 200 days

=> 1 semi-skilled worker can complete 1/200 th of work in one day

10 un-skilled workers can build a wall in 30days

=> 1 un-skilled worker can build a wall in 30 * 10 = 300 days

=> 1 un-skilled worker can complete 1/300 th of work in one day

Given that a team has 2 skilled, 6 semi-skilled and 5 unskilled workers:

2 skilled can complete 2 * (1/100)th of work in one day => 1/50^th

6 semi-skilled can complete 6 * (1/200)th of work in one day => 3/100^th

5 un-skilled can complete 5 * (1/300)th of work in one day => 1/60^th

The team can complete => 1/50 + 3/100 + 1/60 = (6+9+5)/300

= 20/300 = 1/15^th of work in one day

This means team can complete the work in 15 days

Answer (D)