Question

There are some boys and girls in a class. If every girls
mark is decreased by 20 marks then the total average
decreases by 5 marks find the number of boys if the
number of girls is 100
(a) 300 (b) 400 (c) 500 (d) 250​

Answer 1

$Let \: Number \:of \: Boys = x,\\Let \:Sum \:of \: Boys \:Marks = a,\\Sum \:of \:girls \:marks = y\\Number \:of \:girls = 100 \:(given)$

$Average \:marks = \frac{a+y}{100+x}$

/* According to the problem given,

If every girlsmark is decreased by 20 marks then the total averagedecreases by 5 marks find the number of boys*/

$\frac{a+y}{100+x} - 5 = \frac{a+y-2000}{100+x}$

$\implies \frac{a+y}{100+x} - 5 = \frac{a+y}{100+x} - \frac{2000}{100+x}$

$\implies -5 = -\frac{2000}{100+x}$

$\implies 5(100+x) = 2000$

$\implies 100+x = \frac{2000}{5}$

$\implies 100 + x = 400$

$\implies x = 400 - 100$

$\implies x = 300$

Therefore.,

$\red { Number \:of \:Boys } \green {= 300 }$

$Option \: \pink { ( a ) } \: is \: correct$

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