Question : The sum of the two numbers is 37 and the difference between their squares is 185, then the difference between the two numbers is:
Option 1: 10
Option 2: 4
Option 3: 5
Option 4: 3
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Correct Answer: 5
Solution :
Let the two numbers be X and Y.
Given: X + Y = 37 and X
2
– Y
2
= 185
According to the question
X
2
– Y
2
= 185
⇒ (X + Y)(X – Y) = 185
⇒ 37(X – Y) = 185
$\therefore$ X – Y = 5
Hence, the correct answer is 5.
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