Question

Samina spent 1/8 of her money to buy books, 1/5 in purchasing clothes and 1/10 on charity. If she still had Rs 15, more than half of her money, find the amount she had originally.

Answer 1

m = the amount she had originally

She spent:

1 / 8 of her money = m / 8 to buy books

1 / 5 of her money = m / 5 in purchasing clothes

and

1 / 10 of her money = m / 10 in purchasing clothes


She spent total: m / 8 + m / 5 + m / 10


Rest of money = m - ( m / 8 + m / 5 + m / 10 ) = m - m / 8 - m / 5 - m / 10


She still had Rs 15, more than half of her money mean:

Rest of money = m / 2 + 15


So:

m / 2 + 15 = m - m / 8 - m / 5 - m / 10

20 ∙ m / 20 ∙ 2 + 40 ∙ 15 / 40 = 40 m / 40 - 5 ∙ m / 5 ∙ 8 - 8 ∙ m / 8 ∙ 5 - 4 ∙ m / 4 ∙ 10

20 m / 40 + 600 / 40 = 40 m / 40 - 5 m / 40 - 8 m / 40 - 4 m / 40

( 20 m + 600 ) / 40 = ( 40 m - 5 m - 8 m - 4 m ) / 40

( 20 m + 600 ) / 40 = 23 m / 40

Multiply both sides by 40

20 m + 600 = 23 m

Subtract 20 m to both sides

20 m + 600 - 20 = 23 m - 20 m

600 = 3 m

3 m = 600

Divide both sides by 3

m = 600 / 3

m = 200 Rs


Proof:

She spent:

1 / 8 of her money = 200 / 8 = 25 Rs to buy books

1 / 5 of her money = 200 / 5 = 40 Rs in purchasing clothes

and

1 / 10 of her money = 200 / 10 = 20 Rs in purchasing clothes


She spent total: 25 + 40 + 20 = 85 Rs


Rest of money = 200 - 85 = 115 Rs = ( 100 + 15 ) Rs = ( 200 / 2 + 15 ) Rs

Answer 2

One my typo:

not

Subtract 20 m to both sides

20 m + 600 - 20 = 23 m - 20 m4

than

Subtract 20 m to both sides

20 m + 600 - 20 m = 23 m - 20 m