Question

Aseem's expenditure and savings are in ratio 5:1. If his salary is increased by 25% and his saving is increased by 15%. What percent does his expenditure increase?

Answer 1

let the expenditure be 5a and the savings be a 

so total salary = 5a + a = 6a

on 25 % increment 

6a x 25 % + 6a = 6a/4 + 6a =  15a/2 

so increment in the  savings = 15 % 

let the savings amount be b 

 ⇒ (b-a)/a x 100 = 15 

⇒ b = 15 x a/100 + a

⇒ b = 23a/20 

so total expenditure amount = 15a/2 - 23a/20 = 127a/20

so increase = 127a/20 - 5a = 27a/20 

percent increase = 27a/100a x 100 = 27 % ANSWER

Answer 2

old  Salary = T          Expenditure = E           and    savings = S
new salary = T"        new expenditure = E"        new savings = S"

       E :  S = 5 : 1          =>   E = 5 S

       Salary  = T = E + S  = 6 S

        S" = S + 15/100 S = 23 S/20

        T" =   T + T* 25/100 = 5 T /4  =  5*6S/4 = 15 S/2

        T"  =   E" +  S"
         15 S / 2  =  E" + 23 S /20

  =>  E" = 15 S/2 - 23 S /20 = 127 S /20

So expenditure increased from E = 5 S  to  E" = 127S /20
  % increase =  [127/20 - 5] * 100 / 5 =  27 %