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Direction: Read the following question carefully and choose the right answer.
1
In a family there are two children Navya and Reet. The ratio between the present age of Navya and Reet is 5 : 6. After 8 years the ratio of their ages will be 7 : 8. Find their total age of Navya and Reet after 10 years.
» Explain it
E
Let the present age of Navya = 5x, Reet = 6x

After 8 years,

5x + 8 : 6x + 8 = 7 : 8

(5x + 8) 8 : (6x + 8) 7

40x + 64 = 42x + 56

64 – 56 = 42x – 40x

8 = 2x

x = 4

Present age of Navya = 20, Reet = 24

After 10 years the total of their ages = 20 + 10 + 24 + 10 = 64

Hence, option E is correct.
2
Monika, Neha and Bharti are three sister. Monika and Neha are twins. The ratio of sum of the ages of Monika and Neha is same as that of Bharti alone. Three years earlier the ratio of age of Monika and Bharti was 5 : 11. What will be the age of Bharti 7 years hence?
» Explain it
E
Since Monika and Neha are twins so their ages be same. Let their ages be x and and age of Bharti be y, then,

x + x = y        ...(i)

 
and   (x – 3)  =  5
(y – 3) 11

⇒ 11x – 33 = 5y – 15

⇒ 11x – 5y = 18

Now, from equation (i) putting y in terms of x, we get

11x – 10x = 18

⇒  x = 18  

So, the age of Bharti 7 years hence will be 18 + 18 + 7 = 43 years.

Hence, option E is correct.
3
The average age of a group of 15 employees is 24 years. If 5 more employees join the group, the average age increases by 2 years. Find the average age of the new employees. 
» Explain it
D
Method I: Total age of 15 employees = 15 × 24 = 360

Total age of 20 employees = 20 × 26 = 520

Let the average age of 5 new employees be x.

Therefore, the total age of the new employees = 5x

Hence, the total age of 20 employees = 360 + 5x

∴   520 = 360 + 5x

∴   160 = 5x

∴   x = 32

The average age of the new employees = 32

Hence, option D is correct.

Method II:  Average age increased by 2 years i.e. 24 + 2 = 26 years

Total increment in Group's age (15 + 5) × 2 = 40 years

Now, avg age of new employees = 24 +  40  = 32 years
5

4
Five years ago, the age of John was 5 times that of his son. After 5 years,  his age will be 3 times that of his son. After how many years, will he be twice as old as his son?
» Explain it
B
Let the present age of John be x and that of his son be y

Forming equations

x – 5 = 5(y – 5)

x + 5 = 3(y + 5)

After soving we get

x = 55 and y = 15

After how many years, he will be twice as old as son

55 + x = 2 (15 + x)

x = 25 years

The answer can be found by trying options

=   (55 + 25)  = 2
(15 + 25)

Hence, option B is correct.
5
Two years ago, the age of Rajan was 4 times that of his son. After 5 years, the ratio of ages of Rajan to his son will be 5:2. What is the present age of his son?
» Explain it
D
Let age of Rajan be x and that of his son be y
 
So as per the question:
 
(x – 2) : (y – 2) = 4 : 1 or 4 (y – 2)= x – 2 (this is the first equation)
 
(x + 5) : (y + 5) = 5/2 or 5(y + 5)= 2(x + 5) (this is the second equation)
 
Solving both of them we get x = 30 and y = 9
 
So present age of the son is 9 years

Hence, option D is correct.