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- Question
A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
Options- A. 32 years
- B. 36 years
- C. 40 years
- D. 48 years
- Correct Answer
- 40 years
ExplanationLet the mother's present age be x years.Then, the person's present age = ❨ 2 x ❩ years. 5 ∴ ❨ 2 x + 8 ❩ = 1 (x + 8) 5 2 ⟹ 2(2x + 40) = 5(x + 8)
⟹ x = 40.
Problems on Ages
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- 1. Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit?
Options- A. Rs. 9,423
- B. Rs. 10,250
- C. Rs. 12,500
- D. Rs. 10,500 Discuss
Correct Answer: Rs. 10,500
Explanation:
Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.- 2. A and B entered into partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew ¼ of his capital and B withdrew 1⁄5 of his capital. The gain at the end of 10 months was Rs. 760. A's share in this profit is:
Options- A. Rs. 330
- B. Rs. 360
- C. Rs. 380
- D. Rs. 430 Discuss
Correct Answer: Rs. 330
Explanation:
A : B = [ 4x x 3 + ❨ 4x - 1 x 4x ❩ x 7 ] : [ 5x x 3 + ❨ 5x - 1 x 5x ❩ x 7 ] 4 5 = (12x + 21x) : (15x + 28x)
= 33x :43x
= 33 : 43.
∴ A's share = Rs. ❨ 760 x 33 ❩ = Rs. 330. 76 - 3. A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. Calculate the share of B in the profit.
Options- A. Rs. 1900
- B. Rs. 2660
- C. Rs. 2800
- D. Rs. 2840 Discuss
Correct Answer: Rs. 2660
Explanation:
For managing, A received = 5% of Rs. 7400 = Rs. 370.Balance = Rs. (7400 - 370) = Rs. 7030.
Ratio of their investments = (6500 x 6) : (8400 x 5) : (10000 x 3)
= 39000 : 42000 : 30000
= 13 : 14 : 10
∴ B's share = Rs. ❨ 7030 x 14 ❩ = Rs. 2660. 37 - 4. Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
Options- A. 5 : 7 : 8
- B. 20 : 49 : 64
- C. 38 : 28 : 21
- D. None of these Discuss
Correct Answer: 20 : 49 : 64
Explanation:
Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.Then, 14x : 8y : 7z = 5 : 7 : 8.
Now, 14x = 5 ⟺ 98x = 40y ⟺ y = 49 x 8y 7 20 And, 14x = 5 ⟺ 112x = 35z ⟺ z = 112 x = 16 x. 7z 8 35 5 ∴ x : y : z = x : 49 x : 16 x = 20 : 49 : 64. 20 5 - 5. A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives:
Options- A. Rs. 8400
- B. Rs. 11,900
- C. Rs. 13,600
- D. Rs. 14,700 Discuss
Correct Answer: Rs. 14,700
Explanation:
Let C = x.Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
⟹ 3x = 36000
⟹ x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
∴ A's share = Rs. ❨ 35000 x 21 ❩ = Rs. 14,700. 50 - 6. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
Options- A. 16 years
- B. 18 years
- C. 20 years
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: 16 years
Explanation:
Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.Then, (6x + 6) + 4 = 11 (5x + 6) + 4 10 ⟹ 10(6x + 10) = 11(5x + 10)
⟹ 5x = 10
⟹ x = 2.
∴ Sagar's present age = (5x + 6) = 16 years.
- 7. Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?
Options- A. 1 year
- B. 2 years
- C. 25 years
- D. Data inadequate
- E. None of these Discuss
Correct Answer: Data inadequate
Explanation:
Given that:
1. The difference of age b/w R and Q = The difference of age b/w Q and T.
2. Sum of age of R and T is 50 i.e. (R + T) = 50.
Question: R - Q = ?.
Explanation:
R - Q = Q - T
(R + T) = 2Q
Now given that, (R + T) = 50
So, 50 = 2Q and therefore Q = 25.
Question is (R - Q) = ?
Here we know the value(age) of Q (25), but we don't know the age of R.
Therefore, (R-Q) cannot be determined.- 8. Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
Options- A. 24
- B. 27
- C. 40
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: 24
Explanation:
Let the present ages of Sameer and Anand be 5x years and 4x years respectively.Then, 5x + 3 = 11 4x + 3 9 ⟹ 9(5x + 3) = 11(4x + 3)
⟹ 45x + 27 = 44x + 33
⟹ 45x - 44x = 33 - 27
⟹ x = 6.
∴ Anand's present age = 4x = 24 years.
- 9. The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
Options- A. 5 : 2
- B. 7 : 3
- C. 9 : 2
- D. 13 : 4 Discuss
Correct Answer: 7 : 3
Explanation:
Let the ages of father and son 10 years ago be 3x and x years respectively.Then, (3x + 10) + 10 = 2[(x + 10) + 10]
⟹ 3x + 20 = 2x + 40
⟹ x = 20.
∴ Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.
- 10. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
Options- A. 14 years
- B. 18 years
- C. 20 years
- D. 22 years Discuss
Correct Answer: 22 years
Explanation:
Let the son's present age be x years. Then, man's present age = (x + 24) years.∴ (x + 24) + 2 = 2(x + 2)
⟹ x + 26 = 2x + 4
⟹ x = 22.
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