Madhya Pradesh Police Exam Model Paper 7

GIven:
In the 12th innings, Sachin Tendulkar scores = 120 runs
Formula used:
Average = sum of all numbers/total number
Calculation:
Let Sachin Tendulkar, average scores in 11th innings be x
Total runs in 11th innings $=11\times \mathit{x}$
$\Rightarrow 11\mathit{x}$
After increasing the average by 5 runs, new average $=\mathit{x}+5$
⇒ (Total runs in 11th innings + runs in 12th innings)/12 = x + 5
$\Rightarrow \left(11\mathit{x}+120\right)/12=\mathit{x}+5$
$\Rightarrow \left(11\mathit{x}+120\right)=\left(\mathit{x}+5\right)\times 12$
$\Rightarrow 11\mathit{x}+120=12\mathit{x}+60$
$\Rightarrow 12\mathit{x}\mathit{–}11\mathit{x}=120\mathit{–}60$
$\Rightarrow \mathit{x}=60$
New average $=60+5$
⇒ 65 ∴ The new average is 65.
Actually after scoring 120 runs in 12th innings the average increased by 5 runs.
then total increased runs $=12\times 5=60$ runs
Now previous average should be $120-60$
⇒ 60 runs
New average = 60 + increased average
⇒ New average $=60+5$
⇒ 65 runs
∴ The new average is 65.