Question : The product of two numbers is 24 times the difference between these two numbers. If the sum of these numbers is 14, the larger number is:
Option 1: 9
Option 2: 8
Option 3: 7
Option 4: 10
Correct Answer: 8
Solution :
Let the first number be $a$.
So, second number $=(14-a)$
Product of two numbers = 24 × difference of two numbers
$a(14-a) = 24(a-14+a)$
⇒ $14a-a^{2} = 48a-336$
⇒ $a^{2}+34a-336=0$
⇒ $a^{2}+42a-8a-336=0$
⇒ $a(a+42)-8(a+42)=0$
⇒ $(a+42)(a-8)=0$
Since $a$ cannot be negative, $a=8$
So, second number = (14 – 8) = 6
So, the larger number is 8.
Hence, the correct answer is 8.
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