Question

A man saves 1/6 of his salary, spends 1/4 of the remainder on rent and rest on food. What fraction of his salary does he spend on food.​
Ans :5/8​

Answer 1

Answer:

5/8

Step-by-step explanation:

let the whole salary be represented by x

he saves 1/6x

the remainder of the salary being 5/6x

fraction spent on rent = 1/4 of 5/6x = 5/24x

to obtain fraction spent on food, we'd have to subtract the fraction for rent from the remainder of the salary after saving.

5/6x - 5/24x

solving this will result in 15/24x = 5/8x

Answer 2

Step-by-step explanation:

let x denote the salary.

Since saving is 1/6 of the salary,

saving = 1/6x

Since rent is 1/4 of the remaining salary,

rent = 1/4(x - 1/6x) = 1/4x - 1/24x = (6x-x)/24 = 5x/24

Since food is the remaining( that is after saving and paying rent),

food = (x - 1/6x - 5x/24) = (24x - 4x - 5x)/24 = 15x/24

Therefore,

x = saving + rent + food

x = 1/6x + 5x/24 + 15x/24 - - - - - (1)

So,

food = 15/24 * x

food = 15/24 * (1/6x + 5x/24 + 15x/24) using (1)

food = 15/24 * (x)

food = 15x/24

food = 5x/8 (simplying)

Hence for food 5/8 of x is spent.