Question

3
peint.
The average age of Sachin and Ganguli is 35 years. If Kaifi
replaces Sachin, the average age becomes 32 years if Kaif |
replaces Ganguli, then the average age become 38 years. If the
average age of Dhoni and Irfan be half of the average age of
Sachin, Ganguli and Kaif, then the average age of all the fivel
people is:
(a) 28 years
(b) 32 years
(c) 25 years
(d) None of these
​

Answer 1

Answer :-

Average age if all 5 is 28 years [Option (a) ]

Explanation :-

Let the

• Age of Sachin be 's' years

• Age of Ganguli be 'g' years

• Age of Kaif be 'k' years

• Age of Dhoni be 'd' years

• Age of Irfan be 'i' years

Average age of Sachin and Ganguli = 35 years

⇒ Sum of ages/2 = 35

⇒ (s + g)/2 = 35

⇒ s + g = 35(2)

⇒ s + g = 70 ---eq(1)

If Kaif replaces Sachin average age = 32 years

⇒ Average age of Kaif and Ganguli = 32 years

⇒ Sum of ages/2 = 32

⇒ (k + g)/2 = 32

⇒ k + g = 32(2)

⇒ k + g = 64 --eq(2)

If Kaif replaces Ganguli, average age = 38 years

⇒ Average age of Sachin and Ganguli = 38 years

⇒ Sum of ages/2 = 38

⇒ (s + k)/2 = 38

⇒ s + k = 38(2)

⇒ s + k = 76 --eq(3)

Adding eq(1), eq(2) and eq(3)

⇒ s + g + k + g + s + k = 70 + 64 + 76

⇒ 2s + 2g + 2k = 210

⇒ 2(s + g + k) = 210

⇒ s + g + k = 210/2

⇒ s + g + k = 105 --eq(4)

Average age of s, g, k = (s + g + k)/3 = 105/3 = 35

Average age of Dhoni and Irfan = (1/2) * Average age of Sachin, Ganguli and Kaif

= (1/2) * 35 = 35/2

⇒ (d + i)/2 = 35/2

⇒ d + i = (35/2) * 2

⇒ d + i = 35 --eq(5)

Adding eq(4) and eq(5)

⇒ s + g + k + d + i = 105 + 35

⇒ s + g + k + d + i = 140

Average age of all five i.e s, g, k, d, i

= (Sum of ages of all 5)/5

= 140/5

= 28

∴ the average age if all 5 is 28 years [Option (a)]