Age related problems
Age
1. Murali’s present age is half of his father’s age. Before 10 years, his father’s age was thrice his age.
Find the present age of Murali and his father.
(a)16, 32 years (b) 15, 30 years (c)20, 40 years (d)17, 34 years
In the answer choices Murali and his father ages are given and all the choices satisfies the given
condition that Muralis’s present age is half of his father’s age. So we verify which one satisfies the
other condition “Before 10 years, his father’s age was thrice his age”.
Choice - 10 First × 3
16, 32 6, 22 6 × 3 = 18 ≠ 22
15, 30 5, 20 5 × 3 = 15 ≠ 20
20, 40 10, 30 10 × 3 = 30
So, the choice c satisfies the condition. Ans. (c)
Aliter : If x is the present age of Murali, then his father’s present age is 2x.
10 years ago Murali age was x - 10 and his father’s age was 2x - 10.
By the given condition 2x - 10 = 3(x - 10) = 3x - 30
3x - 2x = 30 - 10
x = 20 Ans. (c)
2. Ram is 7 times as old as his daughter Nanthini. After 5 years he will be 5 times as old as his
daughter. What are their present ages? (a)5, 35 (b)6, 42 (c)9, 63 (d)10, 70
In the answer choices Nanthini and his father Ram ages are given and all the choices satisfies the
condition that Ram is 7 times as old as his daughter. So we verify which one satisfies the
another condition “After 5 years, Ram will be 5 times old as his daughter”.
Adding 5 with the given answer choices, age after 5 years 10, 40 ; 11, 47; 14, 68; 15, 75.
Only in 15, 75 the second number is 5 times the first one
So the corresponding given choice is the answer. Ans 10, 70 (d)
Aliter : If x is the present age of Nanthini, then his father’s present age is 7x.
After 5 years Nanthini age will be x + 5 and his father’s age will be 7x + 5.
By the given condition 7x + 5 = 5(x + 5) = 5x + 25
7x - 5x = 25 - 5
2x = 20
x = 10 Ans. (d)
3. A mother is 20 years older than her daughter, 4 years before she was 5 times her daughter's age at
that time. How old is the daughter now? (a)9 (b)12 (c)18 (d)16
In the answer daughter age is given, hence mother age is answer + 20.
4 years ago, mother age = answer + 20 - 4 = answer + 16.
Since the mother was 5 times daughter age at that time, it should be a multiple of 5.
9 + 16 = 25 is a multiple of 5. Ans. 9 (a)
Aliter : If x is the daughter age now then x + 20 - 4 = 5(x - 4)
4x = 16 + 20 = 36
x = 9
4. The difference between the present ages of P and Q is 8 yrs and the ratio of their present ages is
2 : 3 respectively. What is P’s present age? (a)16 yrs (b)24yrs (c)12 yrs (d)30 yrs
Since the ratio of P and Q ages is 2 : 3, Q age > P age.
In the answer age of P is given, hence Q age is answer + 8.
Hence the ratio of ages is answer : answer + 8 and it should be 2 : 3
16 + 8 = 24 and 16 : 24 is 2 : 3. So Ans. (a)
Aliter : If x is the ratio constant then the age of P and Q are 2x, 3x respectively.
Since the difference of ages is 8, 8 = 3x - 2x = x, so P age = 2x = 2 × 8 = 16
5. Ratio of present ages of two persons A and B is 3 : 2 and after four years the ratio of their age
(B : A) becomes 7 : 10. Then find the present age of B?
(a) 20 years (b) 18 years (c) 24 years (d) 36 years (e) 30 years
In the answer age of B is given, hence after 4 years B age is answer + 4.
From the given answer choices after 4 years age of B is
20 + 4 = 24, 18 + 4 = 22, 24 + 4 = 28, 36 + 4 = 40, 30 + 4 = 34
Since after 4 years B age : A age is 7 : 10, after 4 years B age should be a multiple of 7.
Among 24, 22, 28, 40, 34 only 28 is multiple of 7,
so the answer is the corresponding choice 24.
Aliter : If x is the ratio constant then the age of A and B are 3x, 2x respectively.
After 4 years age of A and B are 3x + 4, 2x + 4 respectively.
Hence (2x + 4) / (3x + 4) = 7 / 10
i.e. 21x + 28 = 20x + 40 i.e. x = 12
B age = 2 × 12 = 24
6. If 6 years are subtracted from the present age of Ayush and takes 25% of that then we get the
present age of his only son. 4 years ago, his daughter’s age was 7 years older than his son. Sum of
daughter’s present age and his wife’s present age is 10 years more than Ayush’s present age then
find the present age of Ayush if the average present age of the entire family is 30.25 yr?
(a) 45 year (b) 50 year (c) 60 year (d) 40 year (e) 36 year
In the answer age of Ayush is given, hence son age is (25/100)(answer - 6) = ¼ (answer - 6)
i.e. (answer - 6) = 4 Son age.
So answer - 6 should be a multiple of 4.
From the answer choices, answer - 6 are 45 - 6 = 39, 44, 54, 34, 30.
Among this only 44 is a multiple of 4, so the corresponding choice 50 is the answer. Ans. (b)
Oh! We got the answer without using the other conditions.
Aliter : If Ayush age = x then Son age =(25/100)(x - 6) = ¼ (x - 6),
Daughter age = ¼ (x - 6) + 7, Daughter age + Wife age = x + 10.
30.25 = Average age of entire family = ¼ (Ayush + Son + Daughter + Wife)
= ¼ (x + ¼ (x - 6) + x + 10)
121 = x + ¼ (x - 6) + x + 10 = ¼ (4x + x - 6 + 4x + 40) = ¼ (9x + 34)
9x + 34 = 484
9x = 450
x = 50
7. The ratio of the present age of A to B is 8: 5 and the average of the present age of B and C is
35 years. If five years ago, the sum of ages of A and B is 55 years, then find the difference
between the present age of A and C. (a) 12 (b) 5 (c) 9 (d) 8 (e) 4
Given A : B is 8: 5
½ (B + C) = 35 i.e B + C = 70
Five years ago A and B ages are A - 5, B - 5, hence A - 5 + B - 5 = 55
i.e. A + B = 55 + 10 = 65
Hence C - A = (B + C) - (A + B) = 70 - 65 = 5 Ans. (b)
Oh! A : B is 8 : 5 is not necessary
8. At present a person is 4 times older than his son and is 3 years older than his wife. After 3 years
the age of the son will be 15 years. The age of the person’s wife after 5 years will be:
(1) 48 (2) 45 (3) 50 (4) 42
Since after 3 years son age = 15, Present age of son = 15 - 3 = 12.
Hence present age of the person = 4 × 12 = 48.
Since the person is 3 years older than the wife, wife age = 48 - 3 = 45.
After 5 years age of wife = 45 + 5 = 50 Ans. (3)
9. Two numbers are in the ratio 3 : 5. If 9 is subtracted from the numbers, the ratio becomes
12 : 23. The numbers are (1) 30, 50 (2) 36, 60 (3) 33, 55 (4) 42, 70
In the correct answer, First number - 9 should be a multiple of 12.
From each of the answer choices subtract 9 from the first one.
30 - 9 = 21, 36 - 9 = 25, 33 - 9 = 24, 42 - 9 = 33.
Only 24 is the multiple of 12. Hence the corresponding choice is the answer. Ans. 33, 55 (3)
10. The ratio between two numbers is 4:5. If each number is increased by 9 the ratio becomes
5 : 6. Find the numbers (1) 48, 60 (2) 24, 30 (3) 36, 45 (4) 12, 15
In the correct answer, First number + 9 should be a multiple of 5.
In the answer choices only for 36, 36 + 9 = 45 is a multiple of 5. Ans. (3)
11. The mean age of father and son is 27 years. After 18 years, the father will be twice as old as
his son. Their present ages are (1) 42, 12 (2) 40, 14 (3) 30, 24 (4) 36, 18
All the answer choices satisfy the condition the mean age is 27. But
42 + 18 = 60, 12 + 18 = 30, 60 = 2 × 30
40 + 18 = 58, 14 + 18 = 32, 58 ≠ 2 × 32
30 + 18 = 48, 24 + 18 = 42, 48 ≠ 2 × 42
36 + 18 = 54, 18 + 18 = 36, 54 ≠ 2 × 36
Only Choice (1) satisfies the condition “After 18 years father will be twice as old as son”.
Ans. (1)
12. The sum of ages of a son and father is 56 years. After 4 years the age of father will be three
times that of the son. What is the age of the son?
(1) 10 years (2) 12 years (3) 16 years (4) 18 years
After 4 years both the age of son and father will be increased by 4.
Hence after 4 years sum of ages = 56 + 4 + 4 = 64
But after 4 years father age = 3 son age
So, after 4 years sum of ages = 3 son age + son age = 4 son age.
Hence 4 son age = 64
Son age = ¼ × 64 = 16 Ans. (3)
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