Problems on Numbers Questions for the CAT are part of the Quantitative Aptitude Through Problems on Numbers questions, aspirants are tested to solve questions with fractions. The difficulty level of these questions is easy to moderate.

## What are some CAT Ages Practice Questions?

**Q1**. The ratio of the present ages of a mother and her daughter is 7 : 1. Four years ago, the ratio of their ages was 19 : 1. What will be the mother’s age four years from now?

(a) 42 years

(b) 38 years

(c) 46 years

(d) 36 years

(e) None of these

**Answer 1.** (c)

**Detailed Solution.** Let mother’s age be 7x years. Then, daughter’s age = x years.

7x - 4 / x - 4 = 19 / 1

⇒ 7x – 4 = 19 (x – 4)

⇒ 19x – 7x = 76 – 4

⇒ 12x = 72

⇒ x = 6.

Mother’s age after 4 years = (7x + 4)

= (7 × 6 + 4) years = 46 years

**Q 2**. The ages of Nishi and Vinnie are in the ratio 6 : 5 respectively. After 9 years, the ratio of their ages will be 9 : 8. What is the difference in their ages now ?

(a) 3 years

(b) 5 years

(c) 7 years

(d) 9 years

(e) None of these

**Answer 2**. (a)

**Detailed Solution**. Let Nishi’s age be 6x years. Then, Vinnee’s age = 5x years.

∴ 6x + 9 / 5x + 9 = 9 / 8 ⇒ 8 (6x + 9) = 9 (5x + 9)

⇒ 48x – 45x = 81 – 72

⇒ 3x = 9

⇒ x = 3.

**Q 3.** The present ages of Amit and his father are in the ratio 2: 5 respectively. Four years hence, the ratio of their ages becomes 5: 11 respectively. What was the father’s age five years ago?

(a) 30 years

(b) 35 years

(c) 40 years

(d) 45 years

(e) None of these

**Answer 3**. (b)

**Detailed Solution**. (2y + 4)/(3x + 4) = 5/11 = 11 (2x + 4) = 5 (5x + 4).

⇒ 22x + 44 = 25x + 20

⇒ 3x = 24

⇒ x = 8.

Father’s age 5 years ago = (5x – 5) years

= (5 × 8 – 5) years = 35 years.

**Q 4.** The ratio of the ages of a father and his son is 17: 7 respectively. Six years ago, the ratio of their ages was 3 : 1 respectively. What is the father’s present age ?

(a) 64 years

(b) 51 years

(c) 48 years

(d) Cannot be determined

(e) None of these

**Answer 4.** (b)

**Detailed Solution.** Let the father's age be 17x years. Then, the son's age = 7x years.

17x - 6 / 7x - 6 = 3(7x - 6) = 3(7x - 6) = 17x - 6

⇒ 21x - 18 = 17x - 6

⇒ 4x = 12

⇒ x = 3

∴ Father's present age = 17x years

= (17 × 3) years = 51 years.

## What are the must-do Ages questions for the CAT exam?

**Q 5**. The ages of Shakti and Kanti are in the ratio of 8 : 7 respectively. After 10 years, the ratio of their ages will be 13 : 12. What is the difference between their ages ?

(a) 2 years

(b) 4 years

(c) 8 years

(d) 6 years

(e) None of these

**Answer 5**. (a)

∴ **Detailed Solution**. Let Shakti’s age be 8x years. Then, Kanti’s age = 7x years.

(8x + 10)/(7x + 10) = 13/12 ⇒ 12(8x + 10) = 13(7x + 10)

⇒ 96x + 120 = 91x + 130

⇒ 5x = 10

⇒ x = 2.

Difference between their ages = (8x – 7x) years

= x years = 2 years.

**Q 6**. The ages of A and B are in the ratio 6 : 5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years?

(a) 7 : 6

(b) 8 : 7

(c) 9 : 8

(d) 3 : 4

**Answer 6**. (b)

**Detailed Solution.** A's age = (44 * (6/11)) years = 24 years and B's age

= (44 - 24) years = 20 years.

Ratio of their ages after 8 years = (24 + 8) / (20 + 8) = 32/28 = 8 / 7 = 8:7.

**Q 7**. Farah got married 8 years ago. Today her age is 1(2/7) times her age at the time of her marriage. At present her daughter‘s age is one-sixth of her age. What was her daughter’s age 3 years ago?

(a) 4 years

(b) 3 years

(c) 6 years

(d) Cannot be determined

(e) None of these

**Answer 7.** (b)

∴ **Detailed Solution.** Let Farah’s age 8 years ago be x years. Then, her present age = (x + 8) years.

x + 8 = 9 / 7x ⇒ 7x + 56 = 9x

⇒ 2x = 56

⇒ x = 28.

Farah's age now = (x + 8) years = (28 + 8) years = 36 years.

Her daughter's age now = (1/6 × 36) years = 6 years.

Her daughter's age 3 years ago = (6 - 3) years = 3 years.

**Q 8**. The age of a mother today is thrice that of her daughter. After 12 years, the age of the mother will be twice that of her daughter. The present age of the daughter is:

(a) 12 years

(b) 14 years

(c) 16 years

(d) 18 years

**Answer 8.** (a)

**Detailed Solution.** Let the daughter’s age be x years. Then, the mother’s age = 3x years.

3x + 12 = 2 (x + 12)

⇒ 3x + 12 = 2x + 24

⇒ x = 12.

Present age of daughter = 12 years

**Q 9. **The present age of Mr. Sanyal is three times the age of his son. Six years hence, the ratio of their ages will be 5 : 2. What is the present age of Mr. Sanyal?

(a) 48 years

(b) 50 years

(c) 54 years

(d) 60 years

(e) None of these

**Answer 9**. (c)

**Detailed Solution.** Let the son’s age be x years. Then, Mr. Sanyal‘s age = 3x years.

3x + 6 / x + 6 = (5/2) => 2 (3x + 6) = 5 (x + 6)

⇒ 6x + 12 = 5x + 30

⇒ x = 18.

∴ Present age of Mr. Sanyal = 3x years = (3 × 18) years

= 54 years.

## What were the previous year's CAT Ages questions?

**Q 10. **The average of ages of a man and his daughter is 34 years. If the respective ratio of their ages four years from now is 14 : 5, what is daughter’s present age?

(a) 10 years

(b) 12 years

(c) 18 years

(d) Cannot be determined

(e) None of these

**Answer 10**. (e)

**Detailed Solution**. The average age of a man and his daughter = is 34 years.

Their total age = (34 × 2) years = 68 years.

Let man’s age be x years. Then, daughter’s age = (68 – x) years.

(x + 4)/(68 - x + 4) = 14/5 => 5 (x + 4) = 14 (72 - x)

⇒ 5x + 20 = 1008 – 14x

⇒ 19x = 988

⇒ x = 52.

∴ Daughter’s present age = (68 – 52) years = 16 years.

**Q 11**. The ratio of Rani’s and Komal’s ages is 3: 5 respectively. The ratio of Komal’s and Pooja’s ages is 2 : 3 respectively. If Rani is two-fifths of Pooja’s age, what is Rani’s age?

(a) 10 years

(b) 15 years

(c) 14 years

(d) Cannot be determined

(e) None of these

**Answer 11**. (d)

**Detailed Solution**. Rani's age : Komal's age = 3 : 5 = 3/5 : 1.

Komal's age : Pooja's age = 2 : 3 = 1 : 3/2.

Rani's age : Komal's age : Pooja's age = 3/5 : 1 : 3/2 = 6 : 10 : 15.

Let Rani's age be 6x years. Then, Komal's age = 10x years and Pooja's age = 15x years.

Rani's age = (2/5) of Pooja's age => 6x = (2 / 5) 15x.

Thus, we cannot find the value of x and therefore of 6x.

So, the answer cannot be determined.

**Q 12.** The age of a father 10 years ago was thrice the age of his son. 10 years hence, the father’s age will be twice that of his son. The ratio of their present ages is

(a) 8 : 5

(b) 7 : 3

(c) 9 : 5

(d) 5 : 2

**Answer 12**. (b)

**Detailed Solution**. Let son’s age 10 years ago be x years.

Then, father’s age 10 years ago = 3x years.

Son’s age now = (x + 10) years, Father’s age now

= (3x + 10) years.

(3x + 10) + 10 = 2 [(x + 10) + 10]

⇒ 3x + 20 = 2 (x + 20)

⇒ 3x + 20 = 2x + 40

⇒ x = 20.

Ratio of present ages of father and son

(3x + 10)/(x + 10) = (3 * 20 + 10)/(20 + 10) = 70/30 = 7/3 = 7 : 3

## What were the Ages questions on the CAT 2022 exam?

**Q 13.** The ratio between the ages of Ram and Mohan is 4 : 5 and that between the ages of Ram and Anil is 5 : 6. If the sum of the ages of the three is 69 years, what is Mohan’s age?

(a) 20 years

(b) 24 years

(c) 25 years

(d) 30 years

**Answer 13**. (c)

**Detailed Solution.** Ram's age : Mohan's age = 4 : 5 = 1 : 5 / 4

Ram's age : Anil's age = 5 : 6 = 1 : 6 / 5

Let Ram's age be x years. Then, Mohan's age = 5x/4 years.

And, Anil's age = 6x/5 years.

x + (5x/4) + (6x/5) = 69

=> 20x + 25x + 24x = 1380

=> 69x = 1380

=> x = 20.

Mohan's age = (5x/4) years = (5 × 20) / 4 years = 25 years.

**Q 14.** At present, Suresh’s age is twice the age of his daughter. After 6 years from now, the ratio of the ages of Suresh and his daughter will be 23 : 13. What is the present age of Suresh?

(a) 36 years

(b) 40 years

(c) 46 years

(d) Cannot be determined

(e) None of these

**Answer 14.** (b)

**Detailed Solution**. Let the daughter's age be x years. Suresh's age = 2x years.

2x + 6 / x + 6 = 23/13 => 13 (2x + 6) = 23 (x + 6)

=> 26x + 78 = 23x + 138

=> 3x = 60

=> x = 20.

Present age of Suresh = 2x years

= (2 x 20) years = 40 years.

**Q 15.** The difference between the present ages of Arun and Deepak is 14 years. Seven years ago, the ratio of their ages was 5 : 7 respectively. What is Deepak’s present age?

(a) 35 years

(b) 42 years

(c) 49 years

(d) 56 years

(e) None of these

**Answer 15**. (d)

**Detailed Solution**. Let the ages of Arun and Deepak 7 years ago be 5x years and 7x years respectively. Then,

Arun’s present age = (5x + 7) years, Deepak’s present age

= (7x + 7) years.

∴ (7x + 7) – (5x + 7) = 14

⇒ 2x = 14

⇒ x = 7.

Deepak’s present age = (7 × 7 + 7) years = 56 years.

**Q 16. **Ten years ago, a man was seven times as old as his son. Two years hence, twice his age will be equal to five times the age of his son. What is the present age of the son?

(a) 12 years

(b) 13 years

(c) 14 years

(d) 15 years

**Answer 16**. (c)

**Detailed Solution.** Let son’s age 10 years ago be x years. Then, man’s age 10 years ago = 7x years.

Son’s present age = (x + 10) years, Man’s present age

= (7x + 10) years.

∴ 2 [(7x + 10) + 2] = 5 [(x + 10) + 2]

⇒ 2 (7x + 12) = 5 (x + 12)

⇒ 14x + 24 = 5x + 60

⇒ 9x = 36

⇒ x = 4.

∴ Son’s present age = (x + 10) years = (4 + 10) years

= 14 years.

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