BASIC CONCEPTS
- Age some years ago
- Present age
- Age some years hence
Ex: The difference between the age of two persons ‘A’ & ‘B’ is 16 years, and the age of ‘A’ is three times the age of ‘B’. Find the ratio of their ages after 6 years?
Sol: A : B
3 : 1
Difference 2 = 16
1 = 8
A = 24 yrs B = 8 yrs
Ratio of their ages after 6 years
A : B = (24+6) : (8+6)
= 30 : 14
= 15 : 7
Ex: The sum of the age of father, mother and son is 96 years. After 8 years the mother will be thrice as old as her son and the father will be as old as the mother and son together. Find the present age of the mother?
Sol: Sum ( F+ M + S) = 96 Yrs
Sum (After 8 year) = 96 + 24
= 120 Yrs
F : M : S
4 : 3 : 1
Sum of the ages 8 = 120
Mother‘s age 3 = 45
mother’s Present age = 45 – 8
= 37 Yrs
Ex: A is as much younger than B as he is older than C. If the sum of the age of B and C is 52 years, then find the present age of A?
Sol: B - A = A – C
2 A = B + C
A =
=
…..(B + C = 52)= 26 Yrs
Ex: Amit’s age after 6 years will be three-seventh of his father’s age. Ten year ago the ratio of their ages was 1:5 . What is the age of Amit’s father at present ?
Ex: A is 6 times as old as B. A's age will be twice of C's age after 10 years. If C's 7th birthday was celebrated 3 years ago, what is B’s present age ?
Sol:
A : B = 6 : 1
after 10 years A : C = 2 : 1
at present C is 10 yrs. old.
after 10 yrs. C will be 20 yrs. old.
after 10 yrs. A will be 40 yrs. old.
at present A is 30 yrs. old.
then, 6----------- 30
1-----------5
hence B's present is 5 years.
Ex: The sum of ages of A and B is 45 years. Five years ago the product of their ages was 4 times the age of A at that time. Find the present age of A?
Sol:
A+B = 45
According to question,
A × B : A = 4 : 1 (5 yrs. ago)
i.e. B = 4
At present B = 9
then present age of A = 45 - 9 = 36 years
Ex: Meena got married 8 yrs. ago. Today her age is 4/3 times of her age at the time of marriage. Her daughter's is 1/8 times of her age. Find the sum of their ages after 5 yrs. ?
Sol:
Let the age of Meena at the time of her marriage = 1yr.
Her present age is 1x
= 
= 8
= 81 = 24
Her daughter's age = 32 x
= 4 yrs.sum = 37 + 9 = 46 yrs.
Ex: The ratio of age of A : B is 6 : 5 and the age of each C and D is 9/10 times that of B. Age of F is less than A but greater than B. The ratio of ages of B and E is 2 : 3 also age of A is 3 years less than E. What is the ratio of ages of A and F if all the ages are in integers?
Sol: A: B = 6 : 5
B : E = 2 : 3
A : B : E = 12 : 10 : 15
E - A = 3
3 = 3
12 = 12 (for A)
15 = 15(for E)
10 = 10(for B)
according to question,
F =
= 
A : F = 12 : 11
Ex.: The ratio of the age of a father and a son is 7 : 3 and the product of there age is 756. Then find there ages after 6 years.
Sol.: Let the ratio be x
7x × 3x = 756
21x2 = 756
x2 = 36
x = + 6 , -6 × because age can never be negative
Present age
Father = 7 × 6 + 6 = 48
Sum = 3 × 6 + 6 = 24
Ratio after 6 years = 2 : 1
Ex.: Present ages of two brothers are in the ratio 1 : 2 five years ago it was 1 : 3. What will be the ratio of these ages 5 years hence?
Sol: Let the present age of brothers = x and = 2x
5 year ago their age = (x – 5 ) : (2x – 5) = 1:3
x = 10
after 5 year ratio of their ages = (10 + 5) : (20 +5)
= 3 : 5
Ex.: A man's age is 125% of what is was 10 years ago, but 88
% of what it will be after 10 yeas. What is his present age?125% of (x - 10) = x
88
% of (x+10) = x5/4 (x-10) = 5/6 (x+10)
x = 50 years
Ex.: The sum of the ages of a mother and her daughter is 50 years. Also 5 years ago, the mother's age was 7 times the age of the daughter. What are the present ages of the mother and daughter?
Sol.: Let daughter age = x
mother's age = (50 – x)
5 years ago
7 (x – 5) = 50 –x – 5
8x = 50 – 5 + 35 = 80
x = 10
Daughter age = 10 years
Mother's age = 40 years
Ex: Four years ago, the ratio of A’s age to B’s age was 11:14 and four years later, their ages will be in the ratio 13:16. The present age of A is-
Sol: Let the common ratio = x
Father’s age = 7x and son’s age = 3x
Now, from given conditions
7x × 3x = 756
= 756 , 
= 
= 36 x =
= 6Father’s age = 7 × 6 = 42 yr
Son’s age 3 × 6 = 18 yr
After six year’s
Father’s age = 42 + 6 = 48 yr
Son’s age = 18 + 6 = 24 yr
Required ratio =
= 
= 2 : 1Ex.: The ratio between the present ages of Ram and Prabhat is 4:5. If after 5 years the ratio of the present age of Prabhat and the age of Prabhat at that time is 7:8, what will be the ratio between the present age of Ram and Ram’s age after 4 years?
Sol : Let the present age of Ram be 4x years
Present age of Prabhat = 5x years
=
= 
40x = 35x + 35
40
– 35x = 355x = 35 x = 7
Present age of Ram = 4 × 7 = 28 years.
and age of Ram after 4 years = 28 + 4 = 32 years
Required ratio =
= 7 : 8Ex.: Atul is 30 years younger than his uncle today. 5 years ago Atul was
th times as old as his uncle. How old will Atul’s uncle be 5 years from today?Sol: Let the present age of the uncle be x years
Atul’s present age = (x – 30) years
and uncle’s age 5 years ago = (x – 5) years
Atul’s age 5 years ago = (x – 30 – 5) years = (x – 35) years
(x – 5)
= x – 354x – 140 = x – 5
4x - = - 5 + 140
3x = 135
x =
= 45 yearsAge of uncle after 5 years = 45 + 5 = 50 years
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MAHENDRA GURU