A mother gives pocket money to her three children A, B and C in the ratio 3 : 4 : 5 respectively. Then the father gives ₹ 40 to each child. As a result, the pocket money of A, B and C now has the ratio 5 : 6 : 7 respectively. How much does C get from her mother ?
₹ 80
₹ 100
₹ 120
₹ 60
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CISF-AC-EXE – 2022
Let the initial pocket money from the mother for children A, B, and C be 3x, 4x, and 5x respectively.
After the father gives ₹40 to each child, their pocket money becomes:
A: 3x + 40
B: 4x + 40
C: 5x + 40
The new ratio of their pocket money is 5:6:7.
We can set up a proportion using any two children’s new amounts and their corresponding ratio:
(3x + 40) / (4x + 40) = 5 / 6
Cross-multiply:
6(3x + 40) = 5(4x + 40)
18x + 240 = 20x + 200
240 – 200 = 20x – 18x
40 = 2x
x = 20
The question asks for how much C gets from her mother, which is the initial amount for C.
Initial amount for C = 5x = 5 * 20 = ₹100.
– Add the fixed amount received from the father to each child’s money.
– Use the new ratio to form an equation and solve for the variable.
– Calculate the initial amount for C using the value of the variable.
A: 3(20) + 40 = 60 + 40 = 100
B: 4(20) + 40 = 80 + 40 = 120
C: 5(20) + 40 = 100 + 40 = 140
The new ratio is 100:120:140, which simplifies to 10:12:14, and further to 5:6:7, confirming the value of x is correct.