Question

Kumar and Kavya together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Representing the problem mathematically gives the quadratic equation _____.

• A. x² – 5x + 32 = 0
• B. x² – 40x + 124 = 0
• C. x² – 45x + 324 = 0
• D. x² – 4x+ 32 = 0

Answer 1

The correct option is C

x² – 45x + 324 = 0

Let the number of marbles Kumar had be $x$.

Then the number of marbles Kavya had = $45–x$

The number of marbles left with Kumar, when he lost 5 marbles = $x–5$

The number of marbles left with Kavya, when she lost 5 marbles = $45–x–5$ = $40–x$

$\therefore$ their product = $(x-5)\times (40-x)$

= $40x$ – $x^2-200+5x$

= $-x^2$ + $45x–200$

So, $-x^2$ + $45x–200=124$ (Given that product = 124)

$\Rightarrow$ $-x^2$ + $45x–324=0$

$\Rightarrow$ $x^2$ – $45x+324=0$