# APE 1 - Problem on Ages | Foundation

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**APE 1 - Problem on Ages | Foundation**

The ratio of the ages of Meena and Meera is 4 : 3. The sum of their ages is 35 years. The ratios of their ages after 5 years will be.

- (a)
6 : 5

- (b)
5 : 4

- (c)
7 : 6

- (d)
None of these

Answer: Option B

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**Explanation** :

Let the age of Meena and Meera be 4x and 3x respectively.

∴ 4x + 3x = 35

⇒ x = 5

⇒ Present age of Meena = 20 and that of Meera = 15

Now, their ages after 5 years will be

Meena = 20 + 5 = 25

Meera = 15 + 5 = 20

∴ Rato of their ages after 5 years = 25 : 20 = 5 : 4

Hence, option (b).

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**APE 1 - Problem on Ages | Foundation**

The ratio of the ages of Akash and Prakash are 9 : 10 respectively. If the ratio of their respective ages was 4 : 5 ten years ago, what is the present age of Prakash.

Answer: 20

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**Explanation** :

The ratio of present ages of Akash and Prakash is 9 : 10.

Let the present ages of Akash and Prakash be 9x and 10x respectively.

Their ages after ten year will be

Akash = 9x + 10

Prakash = 10x + 10

∴ $\frac{9\mathrm{x}-10}{10\mathrm{x}-10}$ = $\frac{4}{5}$

⇒ 45x - 50 = 40x - 40

⇒ 5x = 10

⇒ x = 2

∴ The present age of Prakash = 10x = 20 years.

Hence, 20.

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**APE 1 - Problem on Ages | Foundation**

Sandeep's age is one-third his fathers age and two-third his sisters age. What is the ratio of ages of Sameer, his sister and his father respectively.

- (a)
1 : 2 : 3

- (b)
2 : 3 : 6

- (c)
3 : 4 : 9

- (d)
2 : 3 : 5

Answer: Option B

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**Explanation** :

Sandeep's age is two-third his sister's age.

∴ Let Sandeep's age be 2x and his sister's age be 3x.

Now, Sandeep is one-third his father's age,

∴ Sandeep's father's age will be 3 × 2x = 6x

Now, ratio of ages of Sameer, his sister and his fater

= 2x : 3x : 6x

= 2 : 3 : 6

Hence, option (b).

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**APE 1 - Problem on Ages | Foundation**

A father was four times his son's age 5 years ago. At present fater is three times his son's age. Find the sum of the present ages of father and son.

Answer: 60

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**Explanation** :

At present father is thrice son's age.

∴ Let the present ages of father and son be 3x and x.

5 years ago, ages of father and son will be 3x - 5 and x - 5 respectively.

5 years ago, father was four times his son's age.

⇒ $\frac{3\mathrm{x}-5}{\mathrm{x}-5}$ = $\frac{4}{1}$

⇒ 3x - 5 = 4x - 20

⇒ 15 = x

∴ Present age of son = x = 15 and present age of father 3x = 45

⇒ Sum of their present ages = 15 + 45 = 60

Hence, 60

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**APE 1 - Problem on Ages | Foundation**

A man's age if two-fifth the age of his mother. After 10 years he will be half his mothers age. Find the present age of his mother.

- (a)
40

- (b)
45

- (c)
50

- (d)
55

- (e)
None of these

Answer: Option C

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**Explanation** :

At present the man is two-fifth the age of his mother.

∴ Let the present ages of mand and his mother be 2x and 5x.

5 years later, ages of mand and his mother will be 2x + 10 and 5x + 10 respectively.

10 years later, man was half the age of his mother.

⇒ (2x + 10) = 1/2 × (5x + 10)

⇒ 4x + 20 = 5x + 10

⇒ 10 = x

∴ Present age of man = 2x = 20 and present age of his mother 5x = 50

Hence, option (c).

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**APE 1 - Problem on Ages | Foundation**

Rajeev's age after 15 years will be 5 times his age 5 years back. What is the present age of Rajeev?

Answer: 10

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**Explanation** :

Let Rajeev's present age be x years.

∴ Rajeev's age after 15 years = (x + 15) years.

Rajeev's age 5 years back = (x - 5) years.

⇒ x + 15 = 5 × (x - 5)

⇒ x + 15 = 5x - 25

⇒ 4x = 40

⇒ x = 10.

∴ Rajeev's present age = 10 years.

Hence, 10.

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**APE 1 - Problem on Ages | Foundation**

The ages of two persons differ by 16 years. If 6 years ago, the elder one was 3 times as old as the younger one, find their present ages.

- (a)
16, 32

- (b)
10, 26

- (c)
12, 28

- (d)
14, 30

Answer: Option D

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**Explanation** :

Let the age of the younger person be x years.

∴ Age of the elder person = (x + 16) years.

⇒ 3 (x - 6) = (x + 16 - 6)

⇒ 3x -18 = x + 10

⇒ 2x = 28

⇒ x = 14.

∴ Their present ages are 14 years and 30 years.

Hence, option (d).

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**APE 1 - Problem on Ages | Foundation**

The product of the ages of Ankit and Nikita is 240. If twice the age of Nikita is more than Ankit's age by 4 years, what is Nikita's age?

Answer: 12

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**Explanation** :

Let Ankit's age be x years.

∴ Nikita's age = 240/x years.

⇒ 2 × (240/x) = x + 4

⇒ 480 = x^{2} + 4x

⇒ x^{2} + 4x – 480 = 0

⇒ (x + 24)(x - 20) = 0

⇒ x = 20.

Hence, Nikita's age = 240/20 = 12 years.

Hence, 12.

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**APE 1 - Problem on Ages | Foundation**

The present age of a father is 3 years more than three times the age of his son. Three years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father.

Answer: 33

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**Explanation** :

Let the son's present age be x years.

∴ Father's present age = (3x + 3) years

⇒ (3x + 3 + 3) = 2 (x + 3) + 10

⇒ 3x + 6 = 2x + 16

⇒ x = 10.

∴ Father's present age = 3x + 3 = 3 × 10 + 3 = 33 years.

Hence, 33.

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**APE 1 - Problem on Ages | Foundation**

Rohit was 4 times as old as his son 8 years ago. After 8 years, Rohit will be twice as old as his son. What is the sum of their present ages?

- (a)
48

- (b)
52

- (c)
56

- (d)
60

Answer: Option C

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**Explanation** :

Let son's age 8 years ago be x years.

∴ Rohit's age 8 years ago = 4x years.

⇒ Son's age after 8 years = (x + 8) + 8 = (x + 16) years.

⇒ Rohit's age after 8 years = (4x + 8) + 8 = (4x+ 16) years.

⇒ 2(x + 16) = 4x + 16

⇒ 2x = 16

⇒ x = 8.

∴ Son's present age = (x + 8) = 16 years.

and, Rohit's present age = (4x + 8) = 40 years.

Sum of their present ages = 16 + 40 = 56

Hence, option (c).

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**APE 1 - Problem on Ages | Foundation**

One year ago, the ratio of Gaurav’s and Sachin’s age was 6: 7 respectively. Four years hence, this ratio would become 7: 8. How old is Sachin?

Answer: 36

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**Explanation** :

Let Gaurav's and Sachin's ages one year ago be 6x and 7x years respectively.

∴ Gaurav's age 4 years hence = (6x + 1) + 4 = (6x + 5) years.

Sachin's age 4 years hence = (7x + 1) + 4 = (7x + 5) years.

⇒ $\frac{6\mathrm{x}+5}{7\mathrm{x}+5}$ = $\frac{7}{8}$

⇒ 48x + 40 = 49x + 35

⇒ 5 = x

∴ Sachin's present age = (7x + 1) = 36 years.

Hence, 36,

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**APE 1 - Problem on Ages | Foundation**

Vidhan's is as much older than Vidhi as Vidhi is older than Nidhaan. If the sum of the ages of Vidhan and Nidhaan is 18 years, what is Vidhi's age (in years)?

- (a)
10

- (b)
9

- (c)
8

- (d)
7

Answer: Option B

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**Explanation** :

Given in the question:

(Vidhan - Vidhi) = (Vidhi - Nidhaan)

⇒ Vidhan + Nidhaan = 2 × Vidhi

⇒ 18 = 2 × Vidhi

⇒ Vidhi = 9 years.

Hence, option (b).

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