Question

A person X can complete 20% of work in 8 days and another person Y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?

(a) 6

(b) 8

(c) 10

(d) 12

Answer 1

Correct option is (a) 6

X can complete 20% of work in 8 days.

So, X can complete 100% of work in 8 x 5 = 40 days.

Again, Y can complete 25% of work in 6 days.

So, Y can complete 100% of work in 6 x 4 = 24 days

Time required to complete whole work by working together

= \(\frac{40\times 24}{40+24}\) 

= \(\frac {40 \times 24}{64}\)

= 15 days.

Now, time required to complete 40% of the work

= \(\frac{40}{100} \times 15\)

= 6 days.

Answer 2

If person X can complete 20% of the work in 8 days then they can complete 100% of the work in 5 x 8 = 40 days.  And if person Y can complete 25% of the work in 6 days then they can complete 100% of the work in 4 x 6 = 24 days.  Then if T is the Total Time that it would take if X and Y were working together to complete the work we could write:

1/40 + 1/24 = 1/T

Solving we get T = 15 days for both working together to complete the job

To complete 40% of the job it would take 0.40 x 15 = 6 days

So the correct answer is: (a) 6