Question 117

The sum of two numbers is 37 and the difference of their squares is 185, then the difference of the two numbers is

Solution

Let the numbers be $$x$$ and $$(37-x)$$

According to ques,

=> $$(37-x)^2-(x)^2=185$$

Using, $$a^2-b^2=(a-b)(a+b)$$

=> $$(37-x-x)(37-x+x)=185$$

=> $$(37-2x)(37)=185$$

=> $$37-2x=\frac{185}{37}=5$$

=> $$2x=37-5=32$$

=> $$x=\frac{32}{2}=16$$

Thus, second number = $$37-16=21$$

$$\therefore$$ Difference of the two numbers = $$21-16=5$$

=> Ans - (A)

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