A man spends $$\frac{1}{3}$$ of his income on food, $$\frac{2}{5}$$ of his income on house rent, $$\frac{1}{5}$$ of his income on clothes. If he still has Rs. 400 left with him, his income is -

Solution(By Examveda Team)

Let total income is 15x (L.C.M. of 3, 5)
$$\eqalign{ & {\text{Spend on food}} \cr & {\text{ = }}\frac{1}{3} \times 15x \cr & = 5x \cr & {\text{Spend on rent}} \cr & {\text{ = }}\frac{2}{5} \times 15x \cr & = 6x \cr & {\text{Spend on clothes }} \cr & {\text{ = }}\frac{1}{5} \times 15x \cr & = 3x \cr & {\text{Income left }} \cr & = 15x - \left( {5 + 6 + 3} \right)x \cr & = 15x - 14x = x \cr & x = 400 \cr & 15x = 6000 \cr & {\text{Income = 6000 }} \cr} $$