Question

In a fifth match of India and Srilanka played in November 2014.
The sum of one third runs scored by Indian team and one seventh runs scored by Srilankan team is 137.
If India won this match by minimum required run, then find the runs scored by Indian team.

Answer 1

Let the runs scored by India be 'x' and the runs scored by Srilanka be 'y'.
One third runs scored by Indian team $=\frac{x}{3}$.
One seventh runs scored by Indian team $=\frac{y}{7}$
$\therefore \frac{x}{3}+\frac{y}{7}=137$
$\therefore \frac{7x+3y}{21}=137$
$\therefore 7x+3y=2877$ ....... $\left(i\right)$
Also, India won this match by minimum required runs, hence the difference between scores of India and Srilanka will be 1.
$\therefore x-y=1$ ....... $\left(ii\right)$
Multiplying $\left(ii\right)$ by $3$ and $\left(i\right)$ by $1$,
$\therefore 7x+3y=2877$
$\therefore 3x-3y=3$
Adding both the equations,
$\therefore 10x=2880$
$\therefore x=288$
Substituting $x=288$ in $\left(ii\right)$
$\therefore y=287$
Runs scored by the Indian team $=288$