12. The sum of the present ages of a father and son is 53 years. Four years ago, the father's age
was four times the age of the son. Find their present ages.
13. At present Ankit is twice as old as his son. In four years, he will be four times as old as
what his son was 9 years ago. Find the present ages of both of them.
14. Srividya gets a certain amount of money on retirement. She deposits half the money in a
bank, gives her daughter half of the remaining and an additional sum of 6000. She gives
her son the remaining amount which is found to be half of what she gave her daughter.
What is the amount Srividya received on retirement?
Answers
12)Let age of father be x yrs
∴ son = (53-x) yrs
∴ By given condition
x−4=4(53−x−4)
∴x−4=4(49−x)
∴x−4=196−4x
∴5x=196+4
∴x=
5
200
=40yrs
∴ father age = 40 yrs
∴ son age = 53 - 40
=13yrs
13)a = 2s
a + 4 = 4 (s - 9)
a + 4 = 4s - 36
a = 4s - 40
4s - 40 = 2s
2s - 40 = 0
2s = 40
s = 20
a = 2s
a = 2 (20)
a = 40
Ankit is 40 years old and his son is 20 years old!
14)she deposits half of that in the bank.
she deposited 1/2 * x in the bank.
she had 1/2 * x left.
she gives half of that to her daughter plus 6000.
her daughter gets 1/2 * 1/2 * x + 6000.
she has she has 1/2 * x minus 1/2 * 1/2 * x - 6000 left.
she gives that to her son.
that is equal to 1/2 of what she gave to her daughter.
what she gave to her daughter is 1/2 * 1/2 * x + 6000.
what she had left is 1/2 * x minus (1/2 * 1/2 * x + 6000).
this means that 1/2 * x minus (1/2 * 1/2 * x + 6000) = 1/2 * (1/2 * 1/2 * x + 6000).
simplify this to get 1/2 * x minus 1/4 * x - 6000 = 1/2 * (1/4 * x + 6000).
combine like terms to get 1/4 * x - 6000 = 1/8 * x + 3000.
subtract 1/8 * x from both sides of this equation and add 6000 to both sides of this equation to get 1/4 * x - 1/8 * x = 3000 + 6000.
combine like terms to get 1/8 * x = 9000.
multiply both sides of this equation by 8 to get x = 72000.
72000 is what she had originally.
she put half of that in the bank.
36000 went to the bank.
she had 36000 left.
she gave half of that plus 6000 to her daughter.
she gave her daughter 18000 + 6000 = 24000.
she has 12000 left.
she gave that to her son.
12000 that she gave to her son was half of the 24000 that she gave to her daughter.
the solution looks good.
the solution is that she received 72000 on retirement.
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