The ratio of monthly incomes of A and B is 7 : 10. The ratio of their expenditures is 2 : 3. If each of A and B saves ₹ 1,000 per month, then what will be the monthly income of B?
[amp_mcq option1=”₹ 9,000″ option2=”₹ 10,000″ option3=”₹ 15,000″ option4=”₹ 12,000″ correct=”option2″]
This question was previously asked in
UPSC CAPF – 2021
– Let the monthly expenditure of A be 2y and the monthly expenditure of B be 3y.
– Savings = Income – Expenditure.
– For A: 7x – 2y = 1000 (Equation 1)
– For B: 10x – 3y = 1000 (Equation 2)
– We need to solve this system of linear equations for x to find the incomes. Multiply Equation 1 by 3 and Equation 2 by 2 to eliminate y:
3 * (7x – 2y) = 3 * 1000 => 21x – 6y = 3000
2 * (10x – 3y) = 2 * 1000 => 20x – 6y = 2000
– Subtract the second new equation from the first new equation:
(21x – 6y) – (20x – 6y) = 3000 – 2000
21x – 20x = 1000
x = 1000.
– The monthly income of B is 10x.
– Monthly income of B = 10 * 1000 = ₹10,000.
Income of A = 7 * 1000 = ₹7,000
Income of B = 10 * 1000 = ₹10,000
Substitute x=1000 into Equation 1: 7(1000) – 2y = 1000 => 7000 – 2y = 1000 => 2y = 6000 => y = 3000.
Expenditure of A = 2y = 2 * 3000 = ₹6,000. Savings of A = 7000 – 6000 = ₹1,000.
Expenditure of B = 3y = 3 * 3000 = ₹9,000. Savings of B = 10000 – 9000 = ₹1,000.
The savings match the given information, confirming the value of x.