‘A’ and ‘B’ have pocket money in the ratio of 3 : 4. After the day’s w

‘A’ and ‘B’ have pocket money in the ratio of 3 : 4. After the day’s work, ‘A’ earned ₹ 600 while ‘B’ earned ₹ 500. However, ‘A’ spent ₹ 150 and ‘B’ spent ₹ 100 during the day. If they have equal amount of money at the end of the day, then the pocket money ‘A’ had in the morning is:

₹ 150
₹ 200
₹ 250
₹ 100
This question was previously asked in
UPSC CISF-AC-EXE – 2023
Let A’s initial pocket money be 3x and B’s initial pocket money be 4x. At the end of the day, A’s total money is 3x + ₹ 600 – ₹ 150 = 3x + ₹ 450. B’s total money is 4x + ₹ 500 – ₹ 100 = 4x + ₹ 400. Since they have equal amounts at the end, 3x + 450 = 4x + 400. Solving for x, we get x = 50. A’s initial pocket money was 3x, which is 3 * 50 = ₹ 150.
– Represent the initial amounts using the given ratio with a variable (e.g., 3x and 4x).
– Formulate expressions for the final amounts for A and B by adding earnings and subtracting spending.
– Set the final amounts equal to each other based on the problem statement.
– Solve the resulting linear equation for the variable x.
– Calculate the initial pocket money for A using the value of x.
This is a typical word problem involving ratios and linear equations. Careful tracking of money earned and spent for each person is crucial. The phrase “equal amount of money at the end of the day” provides the equation needed to solve for the unknown variable.