Question

Before his last Physics test, Nitish's average for Physics was $33\%$. In his last test he scored $40\%$ which increased his average to $34\%$. What must he score in his next test to increase his average to $35\%$?

• A. 45%
• B. 40%
• C. 44%
• D. None of these

Answer 1

The correct option is D

None of these

Method 1: Equation Approach.

Suppose that Nitish wrote 'n' Physics tests before his last test.
Since his average is $33\%$ in those n tests, the sum of his scores in those tests equal 33n percent.
He then scored $40\%$ in his next test to increase his average to $34\%$.
The sum of all his scores is then equal to 33n+40 percent,giving an average of $\frac{33n+40}{n+1}=34\%$. Solving this equation for n gives n=6.
Thus,if Nitish wants an average of $35$ after 6+2 =8 tests,the sum of his scores should equal $8\times 35\%=280\%$.
After 7 tests the sum of his scores equal $7\times 34\%=238\%,$so he needs to score $280\%-238\%=42\%$in his eighth test.

Method 2: Alligation Approach



So, we can easily determine $X=42\%$