A student spent 2\7 of his pocket money on stationaries,a third on food -stuffs and 5\8 of the remainder on transport.if he had sh.150 left, how much pocket money did he have at the beginning??

Let's denote the student's pocket money as x.

The student spent 2/7 of his pocket money on stationaries, which is (2/7)x.
He then spent a third of the remaining money on food-stuffs, which is (1/3)(5/7)x = (5/21)x.
After spending on stationaries and food-stuffs, the student had (1 - 2/7 - 5/21)x = (11/21)x remaining.

The student then spent 5/8 of the remainder on transport, which is (5/8)(11/21)x = (55/168)x.

After spending on transport, the student had (1 - 2/7 - 5/21 - 55/168)x = (13/168)x left, which is equal to sh.150.

Therefore, (13/168)x = 150
x = 150 * (168/13)
x = 1950

Therefore, the student had sh.1950 as pocket money at the beginning.

Let's assume the initial pocket money as x.

Spent on stationaries: 2/7 - x

Spent on food-stuffs: 1/3 - x

Spent on transport: 5/8 - (x - 2/7 - x - 1/3 - x)

Simplified: 5/8 - (5/21 - x) = 25/168 - x

Total spent: 2/7 - x + 1/3 - x + 25/168 - x

Remaining amount: x - (2/7 - x + 1/3 - x + 25/168 - x)

Given that he had Sh. 150 left:

x - (2/7 - x + 1/3 - x + 25/168 - x) = 150

Solving for x:

x - (18/21 - x + 7/21 - x + 25/168 - x) = 150

x - (40/21 - x + 25/168 - x) = 150

x - (40/21 + 25/168) - x = 150

x - (1040/567 + 225/567) - x = 150

x - 1265/567 - x = 150

(567/1265) - x = 150

x = (150 - 1265) / 567

x = Sh. 330

Therefore, the student's initial pocket money was Sh. 330.