Question

How much is the average salary of 30 assembly workers? The foreman is paid a salary of Rs.12000.
(i) The total salary paid to the 30 assembly workers and the foreman is Rs.312000
(ii) The foreman’s salary is \[120\% \] of the average salary of the 30 assembly workers.

A) Statement (i) alone is sufficient, but statement (ii) alone is not sufficient.
B) Statement (ii) alone is sufficient, but statement (i) alone is not sufficient.
C) Both statements together are sufficient but neither statement alone is sufficient.
D) Each statement alone is sufficient.

Answer 1

Hint:
Here, we are given a data sufficiency question. We need to tell whether the given two statements are sufficient to answer the question or not. We will use both the statements and try to find the average salary of 30 assembly workers. We will choose the appropriate option based on whether we are able to find the average salary using the 2 statements or not.
Formulas used: We will use the following formulas:
1. Average of \[n\]observations is given by \[\dfrac{{{\text{sum of observations}}}}{n}\].
2. If \[b\] is \[x\% \] of \[a\], then \[b\] is given by \[b = \dfrac{{100a}}{x}\].

Complete step by step solution:
We know that the salary of a foreman is Rs.12000 and the total salary paid to the 30 assembly workers and the foreman is Rs. 312000.
We will find the total salary paid to the 30 assembly workers:
\[312000 - 12000 = 300000\]
We will now find the average salary of the 30 assembly workers by substituting 30 for \[n\] and 300000 for sum in the formula \[\dfrac{{{\text{sum of observations}}}}{n}\]:
\[{\text{Average}} = \dfrac{{300000}}{{30}} = 10000\]
We are able to find the average using only the first statement. Hence, the first statement is alone sufficient.
To check for the second statement we will substitute 120 for \[x\] and 12000 for \[a\] in the formula \[b = \dfrac{{100a}}{x}\].
\[b = \dfrac{{100 \times 12000}}{{120}} = 10000\]
We have found the average salary of 30 assembly workers to be Rs. 10000 using only the second statement. Hence, the second statement is alone sufficient.
We can conclude that each statement alone is sufficient to find the average salary.

Hence, option D is the correct option.

Note:
Average is also known as mean. The concept of averages has a lot of practical application in our lives. We can compare 2 groups by looking at their average. Mean has widespread application in research, sports and academics. For example, in sports players are compared using their average score.