Question

The average weight of ‘b’ boys in a group is 63 kg. A boy whose weight is 147 kg joins the group such that the average weight of the group becomes a prime number in between 65 and 91. Find the value of ‘b+1’.

• A. 20
• B. 22
• C. 14
• D. 32
• E. 21

Answer 1

Answer: (E)

21

Answer 2

Sum of the weights of 'b' students = 63b kg
After the new boy joins the group
Sum of the weights of (b + 1) boys = (63b + 147) kg
Therefore, new average age of the group = $\frac{(63b + 147)}{ (b + 1)}$
= $\frac{(63b +63 +84)}{ (b + 1)}$
={ $\frac{63(b + 1)}{ (b + 1)}$}+ $\frac{84}{ (b + 1)}$
= 63 + $\frac{84}{ (b + 1)}$
Since, the new average age is an integer; therefore (b + 1) should be factor of 84
Let b + 1 = 2, then new average age of the group = 63+ ($\frac{84}{2}$) = 105 (not possible)
Let b + 1 = 3, then new average age of the group = 63+ ($\frac{84}{3}$) = 91 (not possible)
Let b + 1 = 4, then new average age of the group = 63+ ($\frac{84}{4}$) = 84 (not a prime number)
Let b + 1 = 6, then new average age of the group = 63+ ($\frac{84}{6}$) = 77 (not a prime number)
Let b + 1 = 7, then new average age of the group = 63+ ($\frac{84}{7}$) = 75 (not a prime number)
Let b + 1 = 12, then new average age of the group = 63+ ($\frac{84}{12}$) = 70 (not a prime number)
Let b + 1 = 14, then new average age of the group = 63+ ($\frac{84}{14}$) = 69 (not a prime number)
Let b + 1 = 21, then new average age of the group = 63+ ($\frac{84}{21}$) = 67 (possible)
Let b + 1 = 42, then new average age of the group = 63+ ($\frac{84}{42}$) = 65 (not possible)
Next all factors will give average less than 70
Therefore, only possible number of students = b + 1 = 21