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

Last updated at April 16, 2024 by Teachoo

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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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