Question

39. On a morning prayer all the students of a school stand in three rows , the first row has 20 % more students than the second row and the third row contains 20 % less students than the second row. If the total number of students in all the rows is 300, then find the number of students in the firs row.

Answer 1

Let the Number of Students in Second row be : S

Mentioned : First row has 20% more Students than Second row

$:\implies$  Number of Students in First row : S + 20% × S

$\mathrm{:\implies Number\;of\;Students\;in\;First\;row : S + \left(\dfrac{20}{100} \times S\right)}$

$\mathrm{:\implies Number\;of\;Students\;in\;First\;row : S + \dfrac{S}{5}}$

$\mathrm{:\implies Number\;of\;Students\;in\;First\;row : \dfrac{6S}{5}}$

Mentioned : Third row has 20% less Students than Second row

$\mathrm{:\implies Number\;of\;Students\;in\;Third\;row : S - \dfrac{S}{5}}$

$\mathrm{:\implies Number\;of\;Students\;in\;Third\;row : \dfrac{4S}{5}}$

Mentioned : Total Number of Students in all the rows is 300

$\mathrm{:\implies \dfrac{6S}{5} + S + \dfrac{4S}{5} = 300}$

$\mathrm{:\implies \dfrac{6S + 4S}{5} + S = 300}$

$\mathrm{:\implies \dfrac{10S}{5} + S = 300}$

$\mathrm{:\implies 2S + S = 300}$

$\mathrm{:\implies 3S = 300}$

$\mathrm{:\implies S = 100}$

$\mathrm{:\implies Number\;of\;Students\;in\;First\;row = \dfrac{6S}{5} = \dfrac{6 \times 100}{5}}$

$\mathrm{:\implies Number\;of\;Students\;in\;First\;row = (6 \times 20)}$

$\mathrm{:\implies Number\;of\;Students\;in\;First\;row = 120}$