Question

Last year the total number of of the students in a school was 5000.This year the number of boys increased by 5% & that of girls by 3% & the total number of students increased by 202.How many boys & girls were there in the school last year?​

Answer 1

Answer:

The number of boys in school last years is 2600

The number of girls in school last years is 2400  .

Step-by-step explanation:

Given as :

Total number of students in the school last year = 5000

The % increase of boys this year = 5%

The % increase of girls this year = 3%

Total number of increase students this year = 202

Let The number of boys in school last years = b

Let The number of girls in school last year = g

According to question

∵ Total number of students in the school last year = 5000

i.e  g + b = 5000                   ..............1

Again

Total number of increase students this year = 202

i.e % increase of girls this year × number of girls in school + % increase of boys this year × number of boys in school  =  202

Or, 3% × g + 5% × b = 202

Or, 3 g + 5 b = 20200                    ............2

Solving eq 1 and eq 2

(3 g + 5 b) - 3 × (g + b)  = 20200 - 3 × 5000

i.e (3 g - 3 g) + (5 b - 3 b) = 5200

Or,  0 + 2 b = 5200

∴   b = $\dfrac{5200}{2}$

i.e  b = 2600

So,  The number of boys in school last years = b = 2600

Put the value of b in eq 1

∵  g + b = 5000

Or,  g = 5000 - b

i.e  g = 5000 - 2600

∴   g = 2400

So,  The number of girls in school last years = g = 2400

Hence, The number of boys in school last years is 2600

And The number of girls in school last years is 2400  . Answer