A and B together can do a work in 2T days and A alone can do the same work in 10 days. If B alone can do the work in 5T days, then find the value of T?

Correct option is D

Information Given:

A and B together can do the work in 2T days

A alone can do it in 10 days

B alone can do it in 5T days

We are to find the value of T

Formula Used:

Work is assumed to be 1 unit

Efficiency = Work / Time

A’s 1-day work = 1/10

B’s 1-day work = 1/(5T)

(A + B)’s 1-day work = 1/(2T)

Explanation:

We know:

A’s 1-day work = 1/10

B’s 1-day work = 1/(5T)

Together:

1/10 + 1/(5T) = 1/(2T)

Take LCM of the left-hand side:

(1/10 + 1/(5T)) = (T + 2)/10T = 1/(2T)

Now, cross-multiply:

(T + 2)/10T = 1/(2T)

Multiply both sides by 10T:

T + 2 = 5

T = 3