The salaries of A,B,and C together amount to Rs 333,if they spend 80%,85% and 75% of their respective salaries. If their savings are 7:6:9,then what are their respective salaries ?
Answers
The respective salaries of A, B, and C are Rs. 105, Rs. 120, and Rs. 108.
• Let the salaries of A, B, and C be a, b, and c respectively.
• Percentage of salary spent by A = 80 %
=> Salary spent by A = 80 % of a = (80 / 100 ) × a = 80a / 100
=> Salary saved by A = a - (80a / 100) = ( 100a - 80a ) / 100 = 20a / 100
Or, salary saved by A = a / 5
• Percentage of salary spent by B = 85 %
=> Salary spent by B = 85 % of b = (85 / 100) × b = 85b / 100
=> Salary saved by B = b - (85b / 100) = (100b - 85b) / 100 = 15b / 100
Or, salary saved by B = 3b / 20
• Percentage of salary spent by C = 75 %
=> Percentage of salary spent by C = 75 % of c = (75 / 100) × c = 75c / 100
=> Salary saved by C = c - (75c / 100) = (100c - 75c) / 100 = 25c / 100
Or, salary saved by C = c / 4
• Given, ratio of the savings of A, B, and C = 7 : 6 : 9
=> Savings of A = 7x
Savings of B = 6x
Savings of C = 9x
• Now,
a / 5 = 7x ; 3b / 20 = 6x ; c / 4 = 9x
Or, a = 7x × 5 ; b = (20 × 6x) / 3 ; c = 9x × 4
Or, a = 35x -(i) ; b = 40x -(ii) ;
c = 36x -(iii)
• According to the question,
35x + 40x + 36x = 333
=> 111x = 333
=> x = 333 / 1111
=> x = 3
• Putting the value of x in equations (i), (ii), and (iii), we get,
a = 35 × 3 = 105
b = 40 × 3 = 120
c = 36 × 3 = 108
• To cross-check,
105 + 120 + 108 = 333 (As given)
• Therefore, the salaries of A, B, and C are Rs. 105, Rs. 120, and Rs. 108 respectively.