Question

A boy multiplied $12345679$ by second, third and seventh multiples of $9$, then the average of their total is……
(A) $444444444$
(B) $44444444$
(C) $4444444$
(D) $444444$

Answer 1

Hint: In the given question, we are given a situation where a boy multiplied a number by some multiples of nine and we have to calculate the mean or average of the total. We can calculate the average of all these products that the boy carried out by dividing the sum of the products by the number of products.

Complete step by step solution:
So, we have to calculate the average of the total when a boy multiplies $12345679$ by second, third and seventh multiples of $9$.
Hence, we can calculate the average of the products that the boy carried out by dividing the sum of products by the number of products as we know that $Average = \dfrac{{Sum\,of\,observations}}{{Number\,of\,observations}}$.
Now, we know that the second multiple of $9$ is $18$, third multiple of $9$ is $27$, and the seventh multiple of $9$ is $63$.
Now, Average \[ = \dfrac{{12345679 \times \left( {2 \times 9} \right) + 12345679 \times \left( {3 \times 9} \right) + 12345679 \times \left( {7 \times 9} \right)}}{3}\]
Now, taking $12345679$ common from the numerator, we get,
 \[ = \dfrac{{12345679\left[ {\left( {2 \times 9} \right) + \left( {3 \times 9} \right) + \left( {7 \times 9} \right)} \right] }}{3}\]
Taking out $9$ common from numerator, we get,
 \[ = \dfrac{{12345679 \times 9 \times \left[ {2 + 3 + 7} \right] }}{3}\]
Cancelling the common factors between numerator and denominator, we get,
 \[ = 12345679 \times 3 \times \left[ {2 + 3 + 7} \right] \]
 \[ = 12345679 \times 3 \times 12\]
Simplifying the calculation, we get,
 \[ = 444444444\]
So, the average of the total is \[444444444\] . Hence, option (A) is correct.
So, the correct answer is “Option A”.

Note: One should take care while doing the calculations in the given questions as it involves a lot of complex and tedious calculations. Also, one should not calculate everything beforehand but wait for common factors to get eliminated first and then carry on with the calculations.