Question

X and Y together complete a task in 4 days, Y and Z together in 5 days. If they work independently, who will finish the work in the least time? ​

Answer 1

X and Y together complete a task in 4 days, Y and Z together in 5 days. If they work independently, who will finish the work in the least time? ​

Step-by-step explanation:

Let Q denotes the work.

Let p, q & r denote the amounts of time  required by X, Y & Z respectively to complete the work Q each working alone. ∴

X, Y & Z in 1 day can complete the amounts of work respectively Q/p, Q/q & Q/r by working alone.

Given:

• (i) X and Y together can complete the work W in 4 days.
• (ii) Y and Z together can complete the work W in 5 days.

From (i) we get:,

4*(Q/p + q/b) = Q or 1/p + 1/q = 1/4 …… (1a)

From (ii) we get :

5*(Q/p + Q/r) = Q or 1/p + 1/r = 1/5 …… (1b)

From (1p) - (1q) we get:

1/p - 1/r = 1/4 - 1/5 = 1/20 or 1/p = 1/20 + 1/r …… (2a)

From (1b) we get, 1/q = 1/5 - 1/c …… (2b)

We know  (1/20 + 1/r) > 1/r > (1/5 - 1/r)

Therefore from (2p) & (2q) we see that,

1/p > 1/r > 1/q or p < r < q …… (2c)

∴ from (2r) we can conclude:

if X, Y & Z work independent of each other, then X will complete the work Q in the least time.