Question

Three workers Sachin, Saurav and Rahul are appointed to do a job. They together started the job but Rahul left after 4 days at that time 46% of the work was completed. The remaining job was completed by Sachin and Saurav in 6 days. The ratio of efficiency of Sachin and Saurav is 5 : 4. Find the number of days required by the slowest worker to complete the entire job alone?
1. 20 days
2. 30 days
3. 25 days
4. 40 days

Answer 1

Correct Answer - Option 4 : 40 days

Let x, y and z be the efficiencies of Sachin, Saurav and Rahul respectively.

According to the question,

⇒  4 × (x + y + z) = 46%      ---- (1)

After 4 days when Rahul left,

⇒  6 × (x + y) = 54%

⇒  (x + y) = 9%      ---- (2)

As we know, the ratio of efficiency of Sachin and Saurav

⇒  x : y = 5 : 4      ---- (3)

So, x = 5% and y = 4%      {from eq. (2) and (3)}

⇒  4 × (9% + z) = 46%      {from eq. (1) and (2)}

⇒  36% + 4z = 46%

⇒ 4z = 10%

⇒  z = 2.5%

Since, Rahul has the least efficiency, so he’s the slowest worker among the three.

Days required by Rahul to complete his work alone = 1/(2.5%) = 40 days