A, B and C together can complete a work in P/ 13 days and A & B together can complete the same work in P/10 days. If B alone can complete the work in P/4 days and days taken by C to complete the work is 20 days more than that of A, then find P.

Explanation

One day work of A, B & C together = 13 𝑃 One day work of A & B together = 10 𝑃 One day work of C = 13 𝑃 - 10 𝑃 = 3 𝑃 Time taken by C alone to complete the work = 𝑃 3 days One day work of A & B together = 10 𝑃 One day work B = 4 𝑃 One day work A = 10 𝑃 - 4 𝑃 = 6 𝑃 Time taken by A alone to complete the work = 𝑃 6 days ATQ, 𝑃 3 − 𝑃 6 = 20 𝑃 6 = 20 P = 120