Question

Indian cricket team won 4 more matches than it lost with New Zealand. If it won
\[\dfrac{3}{5}\] of its matches how many matches did India play?
(a) 8
(b) 12
(c) 16
(d) 20

Answer 1

Hint: In this question, we first need to assume some variables for the number of matches lost and for the number of matches won. Then form an equation between number matches won and lost by India and the form other equation relating the total number of matches and the matches won. Now, on simplifying these two equations formed we can get the value of x and y.

Complete step by step answer:
Now, let us assume that the number of matches won by India is x.
The number of matches lost by India be y.
Now, we can write the total number of matches played by India as x + y.
From the given conditions in the question we get,
\[\begin{align}
  & x=y+4............\left( 1 \right) \\
 & x=\dfrac{3}{5}\left( x+y \right)..............\left( 2 \right)\text{ } \\
\end{align}\]
Let us solve the above equation (2) to get a relation between x and y.
\[\begin{align}
  & \Rightarrow \text{5}x=3\left( x+y \right)\text{ } \\
 & \Rightarrow \text{5}x-3x=3y \\
 & \Rightarrow 2x=3y \\
 & \therefore x=\dfrac{3y}{2}\text{ } \\
\end{align}\]
Now, let's substitute this value of x in the equation (1).
\[\begin{align}
  & \Rightarrow \dfrac{3y}{2}=y+4 \\
 & \Rightarrow \dfrac{3y}{2}-y=4 \\
 & \Rightarrow \dfrac{y}{2}=4 \\
 & \therefore y=8 \\
\end{align}\]
From this we can get the value of x.
\[\begin{align}
  & \Rightarrow x=\dfrac{3y}{2}\text{ } \\
 & \Rightarrow x=\dfrac{3\times 8}{2} \\
 & \therefore x=12 \\
\end{align}\]
The total number of matches played by India:
\[\begin{align}
  & \Rightarrow x+y=8+12 \\
 & \therefore x+y=20 \\
\end{align}\]

Hence, the correct option is (d).

Note: We need to be careful about the result because we were asked to find the total matches played by India. So, we need to add both the matches that were lost and won if not then we will choose the wrong options either (a) or (b).
Instead of assuming that the number of matches lost as y and the number of matches won as x we can directly assume that the total number matches played as x and the number of matches won as y and then simplify accordingly .Both methods give the same result.