Question

A cricketer hits $120$ runs in $150$ balls during a test match. $20\%$ of the runs came in $6s$ , $30\%$ in $4s$ , $25\%$ in $2s$ and the rest in singles. How many runs did he score in singles?
(A) $16$
(B) $4$
(C) $20$
(D) $30$

Answer 1

Hint: For answering this question we will use the given information and calculate the runs scored in each form and then subtract it from the total runs scored or it can be explained as we will add all the percentages of runs scored in each form and subtract it from the total percentage of runs that is $100\%$ and calculate the runs scored in the remaining form that is singles.

Complete step by step answer:
Now considering from the question we have a statement as information which says that a cricketer hits $120$ runs in $150$ balls during a test match, $20\%$ of the runs came in $6s$ , $30\%$ in $4s$ , $25\%$ in $2s$ and the rest in singles.
As we have $20\%$ of the total runs that is $100\%$ came in $6s$ , $30\%$ of the total runs that is $100\%$ in $4s$ , $25\%$ of the total runs that is $100\%$ in $2s$.
So we will have to subtract the sum of percentages of runs scored in each form from the total percentage of runs scored that can be mathematically expressed as $100-\left( 20+30+25 \right)=100-75=25\%$ .
Hence we can say that the rest of the total runs are $25\%$ out of $100\%$ in singles.
$20\%$ of $120$ runs have been scored in the form of $6s$ that is $\dfrac{20}{100}\times 120=24$ runs.
$30\%$ of $120$ runs have been scored in the form of $4s$ that is $\dfrac{30}{100}\times 120=36$ runs.
$25\%$ of $120$ runs have been scored in the form of $2s$ that is $\dfrac{25}{100}\times 120=30$ runs.
$25\%$ of $120$ runs have been scored in the form of singles that is $\dfrac{25}{100}\times 120=30$ runs.
Hence we can conclude that the cricketer had scored $30$ runs in singles.

So, the correct answer is “Option D”.

Note: While answering this type of question we should take care of the calculations. We can solve it another way that is by calculating the runs scored in each form and then subtract it from the total runs scored. That the sum of the runs scored in each of the three forms is $24+36+30=90$ . By subtracting this from the total runs scored that is $120$ we will have $30$ . Hence option D is correct.