The ratio of the incomes of Rama and Ganga is 4 : 3 and the ratio of their expenditures is 3 : 2. If each person saves₹2,700, then find their expenditures, respectively.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. ₹8,100 and ₹5,400.
Let the incomes be 4x (Rama) and 3x (Ganga)
Let the expenditures be 3y (Rama) and 2y (Ganga)
Rama's saving = 4x - 3y = 2700
⇒ 8x - 6y = 5400 .....(1)
Ganga's saving = 3x - 2y = 2700
⇒ 9x - 6y = 8100 .....(2)
So, (9x - 6y) - (8x - 6y) = 8100 - 5400
⇒ x = 2700
Substitute x = 2700 into equation (1),
4(2700) - 3y = 2700
⇒ 10800 - 3y = 2700
⇒ 3y = 8100
⇒ y = 2700
Rama's expenditure = 3y = 3 × 2700 = 8100
Ganga's expenditure = 2y = 2 × 2700 = 5400