Question

The mean monthly salary of 10 members of a group is Rs.1445. one more member whose monthly salary is Rs.1500 has joined the group. Find the mean monthly salary of 11 members of the group.
A.Rs.1550
B.Rs.1950
C.Rs.1050
D.Rs.1450

Answer 1

Hint: To find the mean monthly salary of 11 people, we need to find the total salary of all the 11 people combined. As the average salary of 10 people is given, we will find the total salary of the 10 people and then add the salary of the new person which is added to the group. After this, we will get the total salary of all the 11 people of the group which we can divide by 11 to get their mean monthly salary.

Complete step-by-step answer:
The mean monthly salary in a group of 10 people is Rs.1445. Thus, the total salary of all the members of this group will be given by \[1445 \times 10 = 14450\].
Now, to this group a new member is added who has a monthly salary of Rs.1500. So we will add this new member’s salary to the total salary of the 10-member group to get the total salary of the new 11-member group.
Thus, the total salary of the 11-member group will be \[14450 + 1500 = 15950\].
We will divide this total salary by the number of members which is 11 here to get the mean monthly salary.
Thus, the mean monthly salary will be given by \[\dfrac{{15950}}{{11}} = 1450\].
So, the mean monthly salary of this 11 membered group will be Rs.1450.
Hence, option (D) will be the correct option.

Note: One of the most common mistakes in such a type of question is that we tend to take the average of the mean salary of a 10-membered group and the salary of the newly added member, which is incorrect. Because when we take the average, we should divide the total salary by the total numbers of members, which won’t be the case if we simply try to take the average of the mean salary of the 10-membered group and the salary of the newly added member.