Question 12 - CBSE Class 10 Sample Paper for 2018 Boards - Solutions of Sample Papers for Class 10 Boards

Last updated at Sept. 14, 2018 by

A box contains 12 balls of which some are red in colour. If 6 more red balls are put in the box and a ball is drawn at random, the probability of drawing a red ball doubles than what it was before. Find the number of red balls in the bag.

This is a question of CBSE Sample Paper - Class 10 - 2017/18.

Question 12 A box contains 12 balls of which some are red in colour. If 6 more red balls are put in the box and a ball is drawn at random, the probability of drawing a red ball doubles than what it was before. Find the number of red balls in the bag.Given,
Total balls in the box = 12
Red balls in the box = x
Probability of drawing a red ball = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑑 𝑏𝑎𝑙𝑙𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑎𝑙𝑙𝑠)
= 𝑥/12
If 6 more red balls are put in the box,
Total number of balls = 12 + 6 = 18
Number of red balls = x + 6
Probability of drawing a red balls = (𝑥 + 6)/18
Given, after adding 6 balls, probability of drawing a red ball is
double of what it was before.
∴ New Probability = 2 × Old probability
(𝑥 + 6)/18 = 2 × 𝑥/12
(𝑥 + 6)/18 = 𝑥/6
6 [(𝑥 + 6)/18] = 𝑥
(𝑥 + 6)/3 = 𝑥
𝑥+6 = 3𝑥
6 = 3𝑥−𝑥
6 = 2𝑥
2𝑥 = 6
𝑥" = " 6/2
𝑥 = 3
∴ Number of red balls = x = 3

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.