A cricketer hit 120 runs in 150 balls during a test match. 20% of the runs came in 6's, 30% in 4's, 25% in 2's and the rest in 1's. How many runs did he score in
(i) 6's
(ii) 4's
(iii) 2's
(iv) singles
What % of his shots were scoring ones?
(i) Let the cricketer score w runs in 6's.
$\therefore 20 \%$ of $120=w$
$\Rightarrow \frac{20}{100} \times 120=w$
$\Rightarrow w=24$
(ii) Let the cricketer score $x$ runs in 4 's.
$\therefore 30 \%$ of $120=x$
$\Rightarrow \frac{30}{100} \times 120=x$
$\Rightarrow x=36$
(iii) Let the cricketer score $y$ runs in 2's.
$\therefore 25 \%$ of $120=y$
$\Rightarrow \frac{25}{100} \times 120=y$
$\Rightarrow y=30$
(iv) Let the cricket $e r$ score $z$ runs in 1's.
Since, the cricketer scores the rest of the runs in 1's, we have:
$24+36+30+z=120$
$\Rightarrow z+90=120$
$\Rightarrow z=30$