Time taken by A and B to complete a work is in the ratio 2 : 3. A alone worked for 5 days and left the work then B alone worked for 10 days on the same work, It is found than 70% of the work is completed. Find the time in which they together can complete the work.
1). 10 days
2). 15 days
3). 8 days
4). 200/13 days
Ratio of time taken by A and B to complete a work = 2 ? 3
∴ Ratio of efficiency of A and B = 3 ? 2
Let, efficiency of A = 3x/day and efficiency of B = 2x/day
Let, quantity of total work = a
According to problem,
⇒ 5 × 3x + 10 × 2x = 0.7a
⇒ 0.7a = 35x
⇒ a = 50x
Let, they together do the work in = y days
⇒ y × (3x + 2x) = 50x
⇒ y = 50x/5x
⇒ y = 10
∴ They together will complete the work in = 10 days