[CBSE 2025] A bag contains some red and blue balls . . .

Question : A bag contains some red and blue balls. Ten percent of the red balls, when added to twenty percent of the blue balls, give a total of 24. If three times the number of red balls exceeds the number of blue balls by 20, find the number of red and blue balls.

CBSE 2025

Solution : 

Let the number of red balls = x 

and the number of blue balls = y

ATQ

10% of x + 20% of y = 24 
(10/100)x + (20/100)y = 24
x/10 + 2y/10 = 24
(x+2y)/10 = 24
x+2y = 240 — (1) 

3x-y = 20 — (2) 

Solving equation (1) and (2) 

x + 2y = 240 

[3x - y = 20]×2

x + 2y = 240 

6x - 2y = 40

---------------------
7x + 0 = 280
---------------------
7x=280
x=280/7
x=40

putting in equation (2) 

3(40)-y = 20
120-y=20
120-20 = y
100 = y
y = 100

Hence, number of red balls = 40 and number of blue balls = 100.