P and Q working individually can finish a job in x and y days respectively. P starts the work and they both work on alternate days and the job is finished in 7 days. If Q starts the work and with P working on alternate days. the work gets over in 6 $$\frac{3}{4} $$days. Compare the efficiencies of P and Q.

When P starts the work then job finish in 7 days and when Q starts the work then job finish in  6 $$\frac{3}{4} $$days.

Time taken by P to complete the work = x days

Time taken by P to complete the work = y days

When P starts work then P works 4 days and Q works 3 days.

$$\frac{4}{x} + \frac{3}{y} = 1$$ ---(1)

($$\because$$ work done by P + work done by Q = total work)

When Q starts work then Q works 3 $$\frac{3}{4}$$ and P works 3 days.

$$\frac{3}{x} + \frac{15}{4y} = 1$$ ---(2)

Equation (1) multiply by 3 and equation (2) multiply by 4.

$$\frac{12}{x} + \frac{9}{y} = 3$$ ---(3)

$$\frac{12}{x} + \frac{15}{y} = 4$$ ---(4)

on solving both equations,

y = 6 days

from equation (1)-

$$\frac{4}{x} + \frac{3}{6} = 1$$

$$\frac{4}{x} = 1/2$$

x = 8 days

Total work = efficiency $$\times$$ time

work is same then -

Efficiency of P $$\times$$ 8 = Efficiency of Q $$\times 6$$

$$\therefore$$ P's Efficiency =75% Q's Efficiency