**SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Problem Based on Ages**

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SSC CHSL Study MaterialSSC CHSL Previous PapersSSC CHSL Practice Workbook

In ‘problems based on ages’ usually relationships between the ages or two or more persons at two different time are given and we are required to find the ages of these persons. Such problems can be Solved by the knowledge of ‘Linear Equations’. In these problems there may be three situations

**1.** Age some years ago

**2.** Present age

**3.** Age some years hence

Two of these situations are given and it is required to find the third. The relation between the age of two persons may also be given. Simple linear equations are framed and their solutions are obtained. Sometimes, short-cut methods given below are also helpful in solving such problems.

**Some Useful Facts/Formulae**

- The age of A, t yr ago, was n
_{1}times the age of B and at present A’s age is n_{2}times that of B, then

A’s present age = (n_{1}-1/n_{1}-n_{2})n_{2}t yr and B’s present age = (n_{1}-1/n_{1}-n_{2}) t yr

**Example The age of father is 4 times the age of his son. If 5 yr ago father’s age was 7 times the age of his son at that time, what is father’s present age?**

(a) 36 yr

(b) 40yr

(c) 42yr

(d) 48yr

- The present age of A is n
_{1}times the present age of B. If t yr hence, the age of A would be n_{2}times that of B, then

A’s present age=(n_{2}-1/n_{1}-n_{2})n_{2}t yr and B’s present age=(n_{2}-1/n_{1}-n_{2}) t yr

**Example The age of Mr. Gupta is four times the age of his son. After 10 yr, the age of Mr. Gupta will be only twice the age of his son. Find the present age of Mr. Gupta’s son.**

(a) 6 yr

(b) 5 yr

(c) 4 yr

(d) 8 yr

- The age of A, t
_{1}yr ago, was n_{1}times the age of B. If t_{2}yr, hence A’s age would be n_{2}times that of B, then

**Example 10 yr ago, Anu’s mother was 4 times older than her daughter. After 10 yr, the mother will be twice older than the daughter. Find the present age of Anu.**

(a) 20 yr

(b) 22 yr

(c) 24 yr

(d) 28 yr

- The sum of present age of A and B is S yr. If, t yr ago, the age of A was n times the age of B, then

Present age of A = S_{n}-t(n-1)/n+1 yr and present age of

B =S + t(n- 1)/n+1 yr

**Example The sum of the ages of A and B is 42 yr. 3 yr back, the age of A was 5 times the age of B. Find the difference between the present age of A and B.**

(a) 22 yr

(b) 28yr

(c) 25yr

(d) 24yr

**Reference Corner**

**1. The average age of P, Q and R is 5 yr more than R’s age. If the total ages of P and Q together is 39 yr, then R’s age is SSC (10 + 2) 2014**

(a) 16 yr

(b) 14 yr

(c) 12 yr

(d) 24 yr

**2.The average age of A and B is 20 yr. If A is to be replaced by C, the average would be 19 yr. The average age of C and A is 21 yr. The ages of A, B and C in order (in yr) are SSC (10 + 2) 2013**

(a) 22,18, 20

(b) 22, 20,18

(c) 18, 22, 20

(d) 18, 20, 22

**Practice Exercise**

**1. Sachin was twice as old as Ajay 10 yr back. How old is Ajay today if Sachin will be 40 yr old 10 yr hence? **

(a) 20 yr

(b) 10 yr

(c) 30 yr

(d)None of these

**2. Sister’s age is 3 times that of her brother’s. After 5 yr the sister shall be twice as old as her brother. How many years before, the sister’s age was 6 times of her brother’s age? .**

(a) 1

(b) 3

(c) 5

(d) 10

**3. The average age of the mother and her 6 children is 12 yr which is reduced by 5 yr, if the age of the mother is excluded. How old is the mother?**

(a) 42 yr

(b) 40 yr

(c) 48 yr

(d) 50 yr

**4. A father’s age is three times the sum of the ages of his two children, but 20 yr, hence his age will be equal to the sum of their ages. Then, the father’s age is**

(a) 30 yr

(b) 40 yr

(c) 35 yr

(d) 45 yr

**5. The age of A, B and C together total 185 yr. B is twice as old as A and C is 17 yr older than A Then, The respective ages of A, B and C are**

(a) 40 yr, 86 yr and 59 yr

(b) 42 yr, 84 yr and 59 yr

(c) 40 yr, 80 yr and 65 yr

(d) None of the above

**6. 1 yr ago a father was four times as old as his son. In 6 yr times his age exceeds twice his son’s age by 9 yr. Ratio of their ages is**

(a) 13 : 4

(b) 12 : 5

(c) 11 : 3

(d) 9 : 2

**7. The sum of ages of a father and son is 45 yr. 5 yr ago, the product of their ages was four times the father’s age at that time. The present age of the father is**

(a) 39 yr

(b) 36 yr

(c) 25 yr

(d) None of these

**8. 5 yr ago Mr. Sohanlal was thrice as old as his son and 10 yr, hence he will be twice as old as his son. Mr. Sohanlal’s present age (in yr) is**

(a) 35

(b) 45

(c) 50

(d) 55

**9. If 6 yr are subtracted from the present age of Randheer and the remainder is divided by 18, then the present age of his grandson Anup is obtained. If Anup is 2 yr younger to Mahesh whose age is 5 yr, what is the age of Randheer?**

(a) 84 yr

(b) 48 yr

(c) 60 yr

(d) 96 yr

**10. If 1 is added to the age of the elder sister, then the ratio of the ages of two sisters becomes 0.5 : 1, but if 2 is subtracted from the age of the younger one, the ratio becomes 1 : 3. Find the age of the two sisters. **

(a) 8 yr and 5 yr

(b) 11 yr and 6 yr

(c) 9 yr and 5 yr

(d) 8 yr and 6 yr

**11. The ratio of the ages of the father and the son at present is 7:1. After 4 yr, the ratio will become 4:1. What is the sum of the present ages of the father and the son?**

(a) 29 yr

(b) 35 yr

(c) 32 yr

(d) None of these

**12. Anil is at present one-fourth the age of his father. After 16 yr, he will be one-half age of his father. Find the present age of Anil’s father.**

(a) 40 yr

(b) 36 yr

(c) 32 yr

(d) 28 yr

**13. Honey was twice as old as Vani 10 yr ago. How old is Vani today, if Honey will be 40 yr old 10 yr hence? **

(a) 25 yr

(b) 20 yr

(c) 15 yr

(d) 35 yr

**14. The age of the father 5 yr ago was 5 times the age of his son. At present the father’s age is 3 times that of his son. What is the present age of the father?**

(a) 33 yr

(b) 30 yr

(c) 45 yr

(d) None of these

**15. The age of a man is 3 times that of his son. 15 yr ago, the man was 9 times as old as his son. What will be the age of the man sifter 15 yr?**

(a) 45 yr

(b) 60 yr

(c) 75 yr

(d) 65 yr

**Answers**

**Hints & Solutions**

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