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# AGES SET-1

Q.1 Present ages of Anu and Raj are in the ratio 4:5. Eight years from now the ratio of their ages will be 5:6. Find the present age of Raj ?

### D) 41

Ans. C

Let the present ages of Anu and Raj be 4x years and 5x years respectively.

After eight years. Anu’s age = (4x + 8) years;

After eight years, Raj’s age = (5x + 8) years.

Therefore, the ratio of their ages after eight years =

4x + 8 /  5x + 8

This is given to be 5 : 6

Therefore,

4x + 8/ 5x + 8 = 5/6

Cross-multiplication gives 6 (4x + 8) = 5 (5x + 8)

or 24x + 48 = 25x + 40

or 24x + 48 – 40 = 25x

or 24x + 8 = 25x

or 8 = 25x – 24x

or 8 = x

Therefore, Anu’s present age = 4x = 4 × 8 = 32 years

Raj’s present age = 5x = 5 × 8 = 40 years

Q.2 A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present age of Grandfather ?

### D) 62 yrs

Ans. B

Let the granddaughter’s age be x years. Therefore, grandfather’s age will be

10x years.

According to the question,

Grandfather’s age = Granddaughter’s age + 54 years

10x = x + 54

Transposing x to L.H.S, we obtain

10x – x = 54

9x = 54

x = 6

Granddaughter’s age = x years = 6 years

Grandfather’s age = 10x years = (10 × 6) years = 60 years

Q.3 10 yrs ago the sum of the ages of two brothers was equal to one-third of the age of their father. Elder brother is 2yrs older than the younger . At present the sum of their ages is less than the age of the father by 14yrs. What is the age of the father ?

### D) 49 yrs

Ans. A

Let the age of father, elder son & younger son be x,y & z yrs

Therefore, y-10+z-10 = 1/3(x-10)

Or 3y-30+3z-30 = x-10

Or –x+3y+3z = 50—–i

y-z = 2—–ii

x-(y+z) = 14

x-y-z = 14—-iii

Multiply equation iii by 3 & then add equation I, we get

2x = 92

X=92/2 = 46

Q.4 The age of the father 3yrs ago was 7 times the age of his son. At present the father’s age is five times that of his son. What are the present ages of the father & the son ?

### D) Father’s age=48 yrs , Son’s age=12 yrs

Ans. A

Shortcut:

Sons’s age = T1 (x-1) / (x-y)

18/2 = 9 yrs

In the same way, we have

Father’s age = 45 yrs

Q.5 Sum of the ages of the mother & her daughter is 50 yrs. Also 5 yrs ago, the mother’s age was 7 times the age of the daughter. What are the present ages of the mother & the daughter ?

### D) Mother’s age=39 & Daughter’s age=10 yrs.

Ans. C

Shortcut:

Daughter’s age = S1+T1 (N1-1) / N1+1

50+ 5(7-1) / 7+1

10 yrs

Or Mother’s age = 50-10 = 40 yrs

NOTE: If there will be after…….years like”after 5 years” in place of ago like “5 yrs ago”, then use this formula:

S1-T1(N-1) / N1+1