Question
In 2020, the incomes of A and B were in the ratio 8:5,
and their expenses were in the ratio 5:3. A’s savings in 2020 exceeded B’s savings by ₹5,000. In 2021, A’s expenditure increased by 12%, while his income remained unchanged. If A’s savings in 2021 were ₹2,000 more than B’s savings in 2020, determine B’s expenditure in 2020.Solution
Let the incomes of 'A' and 'B', in 2020, be Rs. '8x' and Rs. '5x', respectively. Let the expenses of 'A' and 'B', in 2020, be Rs. '5y' and Rs. '3y', respectively. Savings of 'A' in 2020 = Rs. (8x - 5y) Savings of 'B' in 2020 = Rs. (5x - 3y) ATQ: (8x - 5y) - (5x - 3y) = 5000 Or, 3x - 2y = 5000 ....... (I) Expenses of 'A' in 2021 = 5y X 1.12 = Rs. '5.6y' So, savings of 'A' in 2021 = Rs. (8x - 5.6y) ATQ: (8x - 5.6y) - (5x - 3y) = 2000 Or, 3x - 2.6y = 2000 ...... (II) On subtracting equation (II) from equation (I), we have; 0.6y = 3000 So, y = 5000 So, expenditure of 'B' in 2020 = 3 X 5000 = Rs. 15,000
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