Question

A cricket player after playing 15 tests scored 124 runs in the 16th test. As a result, the average of his runs is increased by 4. The present average of runs is

• A. 55
• B. 64
• C. 60
• D. 68

Hint:

When an average increases after adding a new term, equate the new average formula with the given condition. Always express in terms of \(n\) and \(n+1\) items for clarity.

Answer 1

The Correct Option is B

Step 1: Assume the initial average.
Let the average runs for the first 15 tests be \(x\).
So, the total runs in 15 tests = \(15x\).
Step 2: Add the 16th test runs.
In the 16th test, he scores 124 runs.
So, the total runs after 16 tests = \(15x + 124\).
Step 3: Write the condition for increased average.
The new average = \(x+4\).
Also, new average = \(\dfrac{15x + 124}{16}\).
\[ \dfrac{15x + 124}{16} = x+4 \] Step 4: Solve the equation.
\(15x + 124 = 16x + 64\)
\(\Rightarrow 124 - 64 = 16x - 15x\)
\(\Rightarrow x = 60\).
Step 5: Find the new average.
New average = \(x+4 = 60+4 = 64\).
\[\boxed{64}\]