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Thrice the square of a natural number decreased by 4 times the number is equal to 50 more than the number. The number is :
Answer & Solution
Correct Answer:
Option
B
Let the number be x
Then,
$$\eqalign{ & \Leftrightarrow 3{x^2} - 4x = x + 50 \cr & \Leftrightarrow 3{x^2} - 5x - 50 = 0 \cr & \Leftrightarrow \left( {3x + 10} \right)\left( {x - 5} \right) = 0 \cr & \Leftrightarrow x = 5 \cr} $$
Then,
$$\eqalign{ & \Leftrightarrow 3{x^2} - 4x = x + 50 \cr & \Leftrightarrow 3{x^2} - 5x - 50 = 0 \cr & \Leftrightarrow \left( {3x + 10} \right)\left( {x - 5} \right) = 0 \cr & \Leftrightarrow x = 5 \cr} $$
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