Question

The Indian cricket team played 20 one-day matches in a particular season of a year and won 25% of the matches they played. If they wanted a minimum success rate of 75%, what is the minimum number of matches they would have to play more?​

Answer 1

$\bf\large\green{\underline{given : }}$

• They played 20 matches and won 25%.

• They want minimum success rate of 75%.

$\bf\large\green{\underline{to \: consider : }}$

■ We have to find the minimum more matches which they have to play to get the success rate of 75%.

■ So, we will consider that they played "x" matches more and won all .

$\bf\large\green{\underline{solution : }}$

■ Total matches played = 20 + x

■ Total matches won = 5 + x

So,

$\\ \bf\red{ \frac{total \: matches \: won}{total \: matces \: played \: } \times 100 = 75 }$

$\sf\large\green{\underline{ }} \frac{5 + x}{20 + x} \times 100 = 75 \\ \\ \sf\large\green{\underline{ }} \frac{5 + x}{20 + x} = \frac{75}{100} \\ \\ \sf\large\green{\underline{ }} \frac{5 + x}{20 + x} = \frac{3}{4} \\ \\ \sf\large\green{\underline{ }}4(5 + x) = 3(20 + x) \\ \\ \sf\large\green{\underline{ }}20 + 4x = 60 + 3x \\ \\ \sf\large\green{\underline{ }}4x - 3x = 60 - 20 \\ \\ \bf\large\blue{\underline{ x = 40 \: matches}}$

∴ They have to play 40 more matches to get the success rate of 75%.

$\bf\large\green{\underline{ verification : }}$

• Total matches played = 20 + 40 = 60
• Total matches won = 5 + 40 = 45

Success rate should come 75%.

$= > \sf\green{\underline{ }} \frac{45}{60} \times 100 \\ \\ = > \sf\green{\underline{ }}{ \frac{4500}{60} }{} \\ \\ = > \bf\large\blue{\underline{ 75\%}}\red{ \: \: \:(verified) }$