The annual income of Rehan is Rs. 672000. He spent 28% of his monthly income on rent. ‘z’% of the remaining monthly income was spent on food by him. If (z-15)% of the remaining monthly income was spent on travelling and remaining money was saved which is equal to Rs. 4032, then find out the numerical value of ‘z’.

Solution

The annual income of Rehan is Rs. 672000. Monthly income of Rehan = 672000/12= Rs. 56000 He spent 28% of his monthly income on rent. ‘z’% of the remaining monthly income was spent on food by him. If (z-15)% of the remaining monthly income was spent on travelling and remaining money was saved which is equal to Rs. 4032. 56000 of (100-28)% of (100-z)% of (100-(z-15))% = 4032 56000 of 72% of (100-z)% of (100-z+15)% = 4032 56 x 72 x (100-z) x (115-z) = 4032000 (100-z) x (115-z) = 1000 Z²  − 215z + 10500 = 0 Z²   − (140+75)z + 10500 = 0 Z²   − 140z - 75z + 10500 = 0 z(z − 140) - 75(z − 140) = 0 (z − 140) (z − 75) = 0 z = 140, 75 There are two possible values of ‘z’. But as per the options the value of z will be 75.