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John and Jivanti Together Have 45 Marbles. Both of Them Lost 5 Marbles Each, and the Product of the Number of Marbles They Now Have is 124. We Would like to Find Out How Many Marbles They Had to Start with - CBSE Class 10 - Mathematics

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Question

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with

Solution

Let the number of John's marbles be x.

Therefore, number of Jivanti's marble = 45 - x

After losing 5 marbles,

Number of John's marbles = x - 5

Number of Jivanti's marbles = 45 - x - 5 = 40 - x

It is given that the product of their marbles is 124.

∴ (x - 5)(40 - x) = 124

⇒ x2 – 45x + 324 = 0

⇒ x2 – 36x - 9x + 324 = 0

⇒ x(x - 36) -9(x - 36) = 0

⇒ (x - 36)(x - 9) = 0

Either x - 36 = 0 or x - 9 = 0

⇒ x = 36 or x = 9

If the number of John's marbles = 36, Then, number of Jivanti's marbles = 45 - 36 = 9

If number of John's marbles = 9, Then, number of Jivanti's marbles = 45 - 9 = 36

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 4: Quadratic Equations
Ex. 4.20 | Q: 2.1 | Page no. 76
Solution John and Jivanti Together Have 45 Marbles. Both of Them Lost 5 Marbles Each, and the Product of the Number of Marbles They Now Have is 124. We Would like to Find Out How Many Marbles They Had to Start with Concept: Solutions of Quadratic Equations by Factorization.
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