Question

A man spends 1/3 of his salary on accomodation and 2/5 of the REMAINDER on food. What fraction is left for other purposes?

Answer 1

• 2/5

Given :

• Fraction of the salary spent on accommodation = 1/3
• Fraction of the remainder salary spent on food = 2/5

Task :

• To work out the fraction left for other purposes

Solution :

In order to find the fraction left for other purposes after spending the salary on accommodation and food, we need to find out the fraction remaining after spending on accommodation and then the 2/5 part of the remainder and add it up to 1/3 and deduct the sum by 1 as the fraction for the whole salary.

Fraction left after spending on accommodation

• 
  `1 - (1)/(3) = (3 - 1)/(2) = (2)/(3) \\`

Fraction spent on food

• 
  `(2)/(3) * (2)/(5) = (4)/(15) \\`

Fraction left for other purposes

`1 - ( (1)/(3) + (4)/(5) ) = 1 - ( (5 + 4)/(15) ) = 1 - (9)/(15) = (15 - 9)/(15) = (6)/(15) = (2)/(5) \\`

Therefore, the fraction left for other purposes is 2/5.