Discussion
The product of the ages of Syam and Sunil is 240. If twice the age of Sunil is more than Syam's age by 4 years, what is Sunil's age?
Answer: C
Let age of Sunil = \(x \) years and age of syam be = \(y\) years
\(x y = 240 ⋯ ( 1 )\)
\(2 x = y + 4\)
\(⇒ y = 2 x − 4\)
\(⇒ y = 2 ( x − 2 ) ⋯ ( 2 )\)
Substituting equation \((2)\) in equation \((1)\) we get ,
\(x × 2 ( x − 2 ) = 240\)
\(⇒ x ( x − 2 ) = \) \(\frac{240}{2}\)
\(⇒ x ( x − 2 ) = 120 ⋯ ( 3 )\)
We got a quadratic equation to solve.
Always time is precious and objective tests measure not only how accurate you are but also how fast you are. We can solve this quadratic equation in the traditional way.
But it is more easy to substitute the values given in the choices in the quadratic equation (equation 3) and see which choice satisfy the equation.
Here, option A is 10. If we substitute that value in the quadratic equation,
\(x ( x − 2 ) = 10 × 8\) which is not equal to 120
Now try option B which is 12. If we substitute that value in the quadratic equation,
\(x
(
x
−
2
)
=
12
×
10
=
120
\) See, we got that \(x=12\)\
Hence Sunil's age = 12
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