Question : Select the number that will come in place of the question mark (?) in the following mathematical statement.
49 × 57 – 41 × 18 = (?)2 × 3 + 1380
Option 1: 15
Option 2: 21
Option 3: 3
Option 4: 7
Correct Answer: 15
Solution :
49 × 57 – 41 × 18 = (?)
2
× 3 + 1380
On simplifying the left-hand side of the equation,
49 × 57 – 41 × 18 = 2793 – 738 = 2055
This means that (?)
2
× 3 + 1380 = 2055
On simplifying,
(?)
2
× 3 = 2055 - 1380 = 675
⇒ ? = $\sqrt{\frac{675}{3}}$ = 15
$\therefore$ The number that will come in place of the question mark (?) in the given mathematical statement is 15.
Hence, the correct answer is 15.
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