Question

In a particular month, Ezhil spent one-fifth of her salary on shopping. Two-fifth of the remaining she gave to her sister. If she has Rs 11 , 040 left, what was her salary in that month?

Answer 1

Her salary = Rs 23000

Explanation:

In a month, Ezhil spent 1/5 of her salary on shopping.

Let

Her salary = a

she spent 1/5 of a on shopping

Amount spent on shopping = 1a/5

She gave 2/5 of the remaining to her sister .

The remaining money = a - 1a/5 = 5a - a/5 = 4a/5

She gave 2/5 of 4a/5 to her sister. Therefore,

The amount she gave to her sister = 2/5 × 4a/5 = 8a/25

Out of her salary she is left with Rs 11040 .Therefore,

a - 1a/5 - 8a/25 = 11040

25a - 5a - 8a/25 = 11040

12a/25 = 11040

12a = 11040 × 25

12a = 276000

divide both sides by 12

a = 276000/12

a = 23000

Her salary = Rs 23000

Answer 2

`Salary = Rs23000`

Explanation:

Given

`Shopping = (1)/(5)`

`Sister = (2)/(5)R`

`Left over = Rs11,040`

Required

Her salary in that month

Given that she spent
`(1)/(5)` of her salary on shopping, this implies that she has
`(4)/(5)` of her salary left

From what's left, she gave her sister
`(2)/(5)`

This means she gave her sister
`(2)/(5) * (4)/(5)`

Sister =
`(8)/(25)`

Calculating a fraction of what's left

`Left over = 1 -Shopping - Sister`

`Left over = 1 - (1)/(5)- (8)/(25)`

`Left over = (25 - 5 - 8)/(25)`

`Left over = (12)/(25)`

Recall that she has Rs11,040

This means that

`(12)/(25) of Salary = Rs11,040`

Multiply both sides by
`(25)/(12)`

`(12)/(25) * (25)/(12) * Salary = Rs11,040 * (25)/(12)`

`Salary = Rs11,040 * (25)/(12)`

`Salary = (Rs276000)/(12)`

`Salary = Rs23000`

Hence, her salary for that month was Rs23000