Direction: Read the following question carefully and choose the right answer.
1
The sum of the ages of Kidambi and Srikanth 14 years hence will be equal to 2 times their present age. If at present Kidambi is 8 years elder to Srikanth, then what are their present ages?
» Explain it
C
Let the present ages of Kidambi and Srikanth be x years and y years respectively.
 
As per the question,
 
(x + 14) + (y + 14) = 2(x + y)
 
x + y + 28 = 2x + 2y
 
x + y = 28    .....(i) 
 
Also,
 
y + 8 = x
 
x – y = 8       .....(ii)
 
Solving eqns (i) and (ii), we get
 
x = 18 and y = 10 
 
Therefore, Present ages of Kidambi and Srikanth is 18 years and 10 years respectively
 
Hence, option C is correct.
2
A family consists of paternal grandparents, parents and three grandchildren. The average age of the grandparents is 70 years, that of the parents is 40 years and that of the grandchildren is 10 years. What is the average age of the family?
» Explain it
B
The family consists of grandparents, parents and three grandchildren.

So, the number of family members = 2 + 2 + 3 = 7

We know,

Average of quantities =  Sum of all quantities
No. of quantities

The average age of the grandparents is 70 years. So, the total age of the grandparents = 70 × 2 = 140 years

The average age of the parents is 40 years. So, the total age of the parents = 40 × 2 = 80 years

The average age of the grandchildren is 10 years. So, the total age of the grandchildren = 10 × 3 = 30 years

∴  The total age of the family members = 140 + 80 + 30 = 250 years.
∴  The average age of the family =  250  = 35 5  years
7 7

Hence, option B is correct.
3
Mayank said to his friend “If you subtract 18 from my age the two digits of my age will reverse their positions. Also my age is six less than 8 times the sum of digits of my age”. Find Mayank's age.
» Explain it
E
Let Mayank's age be (10x + y) years
 
Age by reversing the digits = (10y + x) yrs
 
Now, 10x + y − 18= 10y + x
 
9x – 9y = 18
 
x – y = 2..................(1)
 
Also,
 
10x+y = 8(x+y) – 6
 
2x – 7y = –6..........… (2)
 
Solving equations (1) and (2),
 
x = 4 , y = 2
 
Therefore, Mayank's age = 10x + y
 
= 10(4) + 2
 
= 42 years
 
Hence, option E is correct.
4
If the average age of a class is 15 (including the age of the teacher); that of the boys is 10 and if the age of the teacher is 13 more than the average age of the girls , then what is the average age of the girls, given that the number of boys and girls is the same?
» Explain it
E
Let the number of boys = the number of girls = n

Hence, total age of boys = 10n

Let the average age of girls = x

Hence, total age of girls = nx

Total age of the class = 10n + nx + x + 13 

Total number of people in the class = n + n + 1 = 2n + 1

Average age of the class =  (10n + nx + x + 13)  = 15
(2n + 1)

Since this is a single linear equation in two variables, a unique solution can't be found.

Therefore, the average age of the girls cannot be determined.

Hence, option E is correct.
5
There are three Pathan brothers Yusuf Pathan, Irfan Pathan and Saddam Pathan. The sum of the squares of the their ages (in completed years) is 325. If the product of their ages does not exceed 1000, find the age (in years) of the youngest brother.
» Explain it
A
Let the ages of the 3 brothers in completed years be x, y, z.

x2 + y 2 + z2 = 325            .......(i)

Clearly, the three numbers have to be less than 18 since the square of 18 itself is 324.

By trial, we see that 325 = 152 + 82 + 62 or 122 + 102 + 92

As the product of the ages is less than 1000, the ages have to be 6, 8, 15

The youngest is 6.

Hence correct option (A) is correct.