Question

P and Q together can complete a piece of work in 18.75 days while Q and R together can complete the same work in \(27\frac{3}{{11}}\) days. If Q is 20% more efficient than R, then, in how many days will P and R together complete the same work?
1. 20 days
2. 15 days
3. 10 days
4. 25 days
5. 24 days

Answer 1

Correct Answer - Option 1 : 20 days

Given:

P + Q = 18.75 days = 75/4 days

Q + R = 27(3/11) days = 300/11 days

The ratio of efficiency of Q and R = 120 : 100 = 6 : 5

Concept used:

In this type of time and work question, we assume the total work to be done as the LCM of the number of days taken to each of the persons to complete the work.

Formula used :

Total work = Efficiency × Number of days

CALCULATION :

Suppose the total work is (LCM of 75/4 and 300/11) i.e., 300 units.

One day work by (P + Q) = 300/(75/4) = 16 units

One day work by (Q + R) = 300/(300/11) = 11 units

Also given, ratio of efficiency between Q and R = 6 : 5

So, the ratio of efficiency of P and Q = 10 : 6

∴ One day work by (P + R) = 10 + 5 = 15 units

According to question –

The work is completed by (P + R) together in 300/15 days = 20 days