Subject: General Aptitude · Chapter: Problems on Numbers · Exam: · Marks: · Difficulty:
The sum of two numbers is 75 and their difference is 25 . The product of the two numbers is: [SSC-CHSL (10 +2) Exam, 2015]
(a)1350
(b)1250
(c)125
(d)1000
Answer
Answer (as printed): B
Explanation
Let the numbers be $a$ and $b$. According to the question, $a+b=75$ and $a-b=25$. $(a+b)^{2}-(a-b)^{2}=4ab \Rightarrow 75^{2}-25^{2}=4ab$. Since $a^{2}-b^{2}=(a+b)(a-b)$, we get $4ab=(75+25)(75-25)=100\times50 \Rightarrow ab=\frac{100\times50}{4}=1250$.
Explanation as extracted from the printed page; notation may be imperfect.