10 years ago the age of a father was thrice of his son, and after 10 years it will be twice of his son’s age. Then what is the ratio of their present ages?
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Solution
Let present age of son = x years
and of father = y years
So 3(x – 10) = (y –10)
⇒ 3x – 30 = y – 10
⇒ 3x – y = 20 – (i)
10 years after = (y + 10) = 2 (x+10)
⇒ y +10 = 2x + 20
⇒ 2x – y = – 10 – (ii)
x = 30 and y = 70
So required ratio = 70 : 30
= 7 : 3
The age of A and B is 40 and 60 years respectively. How many years ago their age was in the ratio of 3 : 5?
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Solution
let x years ago the ratio was 3 : 5
⇒
⇒ 200 – 5x = 180 – 3x
⇒ 2x = 20
⇒ x = 10 years
Four years ago a mother was 3 times elder than her daughter. If sum of present ages of mother and daughter is 60 years, then what will be present age of daughter?
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Solution
4 years ago daughter :- x years
mother :- 3x years
Present (x + 4) + (3x + 4) = 60
=> x = = 13
∴ Present age of daughter = 13 + 4 = 17 year
The ratio of a son’s age to his father is 3 : 11. if differences of their ages is 24 years. Then the ratio of their ages after 3 years will be?
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Solution
The difference ⇒ (11 – 3) x = 24
⇒ x = 3
Present ages = 9, 33 years
3 years after ratio = 12 : 36
= 1 : 3
At present the ratio of the ages of Anand and Milind is 4: 7 respectively. 6 years hence it will be 7: 10 respectively. What is the present age of Milind?
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Solution
Present ratio of their ages is 4: 7 (So their present ages will be 4x, 7x)
After six years it will be of 7: 10
⇒ (4x + 6): (7x + 6) = 7: 10
⇒ 40x + 60 = 49x + 42 (Cross Multiplication)
⇒ 9x = 18
⇒ x = 2
So milind’s present age will bse 7 × 2 = 14 years
The product of the ages of A and B is 240. If twice the age of B is more than A’s age by 4 years, then difference between the ages of A and B is ?
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Solution
Let A’s age be x years. Then B’s age = years.
∴ 2× -x = 4 ⇔ x = 20.
⇔ (x + 24) (x – 20) = 0 ⇔ x = 20.
Hence, B’s age = (240/20) years = 12 years.
and A's age is 240/12 = 20 years
so the required difference of ages is = 20-12 = 8 years
Abhi is 30 years younger than his mother Jaya. Five years ago, Abhi was as old as his mother was. How old is Abhi today?
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Solution
5 years ago Let Abhi and Jaya's Ages = x and 4x
(4x + 5) – (x + 5) = 30 ⇒ x = 10
Abhi's present Age = 10+5 = 15 years
At present, the ratio between the ages of Anand and Dinesh is 4: 3. After 6 years, Anand’s age will be 26 years. Then what will be the ratio between the ages of Anand and Dinesh after 6 years?
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Solution
Let the present age of Anand and Dinesh be 4x years and 3x years respectively. Then, 4x + 6 = 26 ⇔ 4x = 20 ⇔ x = 5.
Dinesh’s age = 3x = 15 years,
and Anand's age is = 4 × 5 =20 years
so after 6 years the the corresponding ages will be 26 and 21 years respectively.
so required ratio is ⇒ 26 : 21
The ratio of ages of Nikita and Pallavi is 2 : 5, after 8 years the ages will be in the ratio of 1 : 2. The difference in their present ages is.
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Solution
4x + 16 = 5x +8
⇒ x = 8
Difference in present age = 8 × 3 = 24 years
Six years ago A was x times as old as B was. If A is 17 years old now, then what will be age of B in terms of x?
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Solution
6 years ago let age of B was P years
So age of A = x p
at present A = xp + 6 = 17 years
⇒ x p = 11
at present age of B = P + 6
⇒ years