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# AGES SET-3

Q.1 Total age of some 7 years old & some 5 years old children is 60 yrs. If a team is to be selected from these children such that their total age is 48 years, in how many ways can it be done ?
A) 2
B) 3
C) 4
D) 1
Ans. D
7*4+5*4=28+20
=48

Q.2 At present ages of a father & his son are in the ratio of 7:3 & they will be in the ratio of 2 : 1 after 10 years. Then the present age of father is :

A) 77

B) 56

C) 70

D) 42

Ans. C

Shortcut:
Father’s age = x*t (a-b)/ difference of cross product
Or x =7
t=10
a=2
b=1
therefore,
7*10(2-1)/1
=70

Q.3 The present ages of A and B are in the ratio 2 : 3 and the ages of A and C are in the ratio 3 : 4. If the sum of the present ages of A, B and C is 92 years, how many years will it take by B and C to get their ages in the ratio 10 : 9?

A) 2

B) 4

C) 5

D) 6

Ans. B

A : B = 2 : 3 = 6 : 9 (Note: In this since A is common that’s why we have multiplied “2 with 3” & “3 with 9”)

A : C = 3 : 4 = 6 : 8 (Multiplied “3 with 2” & “4 with 2”)

? A : B : C = 6 : 9 : 8
? A age = × 92 = 24 years
B age = × 92 = 36 years
C = × 92 = 32 years
After x years, =
? x = 4 years

Q.4 The sum of ages of a son & father is 56 years. After 4 years, the age of father will be three times that of the son. Their ages respectively are

A) 12 & 44 yrs

B) 16 & 42 yrs

C) 16 & 48 yrs

D) 18 & 36 yrs

Ans. A

Shortcut:
Son’s age=S1+t2(N-1)/N+1 [When age is in years ago]

But in this question use this formula because [It is given after years]

Son’s age= S1-t2(N-1)/N+1

Therefore,
Son’s age is 56-4*2/4=12 where N= 3 as it is given three times

Now, for father’s age=

It is given in Question ,
the sum of ages of a son & father is 56 years

Then,12 + father’s age = 56

Father’s age = 56-12= 44

Other explanation:

Suppose the age of father be a yrs
Then the age of the son = (56-a)
After four yrs the age of the father would be (a+4) yrs & the age of the son would (56-a+4)
Now (a+4) = 3(56-a+4)
(a+4) = 180 – 3a
a = 44 yrs
So, the age of father = 44 yrs
& the age of son = 56-44
= 12 yrs

Q.5 The average age of three girls is 16 years. If their ages are in the ratio 4 : 5 : 7, the age of the youngest girl is :

A) 21

B) 15

C) 16

D) 12

Ans. C
Let the ages of three girls be 4x, 5x, 7x (ratio 4 : 5 : 7 is given)
Average age of the three girls = 16 years
Average age = = 16
16x = 16 3
x = 3.
Age of the youngest girl = 4x = 4 3 = 12 years.

Q.6 The ratio of the ages of two persons (A and B) is 2 : 3 and that of (B and C) is 4 : 5. If the average age of all the three is 35 years. What is B’s age?

A) 24

B) 36

C) 40

D) 30

Ans. B

Total age of A + B + C = 35 × 3 = 105
= ? A =
= ? C =
? + B + = 105
? B = 36 years.