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. How many marbles did they have to start with?

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

9 and 36

10 and 30

11 and 35

15 and 20

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Given that John and Jivanti together have 45 marbles.
After losing 5 marbles each, the product of the number of marbles they now have is 124.
Let the number of marbles John originally had = x.
The number of marbles Jivanti had = 45 – x.
The number of marbles left with John, when he lost 5 marbles = x – 5 … (1)
The number of marbles left with Jivanti, when she lost 5 marbles is,

\Rightarrow

45 – x – 5

\Rightarrow

40 – x … (2)
According to the question, the product of (1) and (2) is 124.

⇒ (x − 5) (40 − x) = 124

Convert the equation into the standard equation form.

⇒ (x − 5) (40 − x) = 124 ⇒ 40 x − x 2 − 200 + 5 x = 124 ⇒ x 2 − 45 x + 324 = 0 ⇒ x 2 − 36 x − 9 x + 324 = 0 ⇒ x (x − 36) − 9 (x − 36) = 0

Factoring the equation to get two linear factors, we get
(x – 9) (x – 36) =0.
Equating each factor to zero to find the value of x,
x – 9 = 0 or x – 36 = 0.
Thus, x = 9 and x = 36 are two roots of the equation