SSC MTS 2022 PYQ — Question 52

The correct answer is Option 2 i.e. $\left ( \frac{2ab}{a+b}\right )$.

Average of b numbers = Sum of b numbers/b

Average of b numbers = $\left [\frac{b(b+1)}{2b} \right ]$

Average of b numbers = (b + 1)/2

According to the question,

Average of b numbers = a

⇒ a = (b + 1)/2

⇒ 2a = (b + 1)

Average of a numbers = Sum of a numbers/a

Average of numbers = $\left [\frac{a(a+1)}{2a} \right ]$

Average of a numbers = (a + 1)/2

According to the question,

Average of a numbers = b

⇒ b = (a + 1)/2

⇒ 2b = (a + 1)

Now,

Average of all the a and b numbers taken together = (Sum of a numbers + Sum of b numbers/a + b)

Average of all the a and b numbers taken together = $\frac{\left [\frac{a(a+1)}{2}+ \frac{b(b+1)}{2} \right ]}{a+b}$

Putting the values of (a + 1) and (b + 1):-

Average of all the a and b numbers taken together = $$$\left ( \frac{ab+ab}{a+b}\right )$

Average of all the a and b numbers taken together = $\left ( \frac{2ab}{a+b}\right )$