# Moderate Number System Solved QuestionAptitude Discussion

 Q. $a, b, c, d$ and $e$ are five consecutive numbers in increasing order of size. Deleting one of the five numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of the following numbers was deleted?
 ✖ A. a ✖ B. b ✔ C. c ✖ D. d ✖ E. e

Solution:
Option(C) is correct

Since $a, b, c, d$ and $e$ are consecutive numbers in the increasing order,
We have $b = a + 1$, $c = a + 2$, $d = a + 3$ and $e= a + 4$.

The sum of the five numbers is:
$a + ( a + 1) + ( a + 2) + ( a + 3) + ( a + 4) = 5 a + 10$

Now, we are given that the sum decreased by 20% when one number was deleted.
Hence, the new sum should be:
\begin{align*} &=(5 a + 10)\left(1 - \dfrac{20}{100}\right) \\ &= (5 a + 10)\left(1 - \dfrac{1}{5}\right)\\ &= (5 a + 10)\left(\dfrac{4}{5}\right)\\ &= 4 a + 8. \end{align*}

Now, since $\text{New Sum = Old Sum - Dropped Number}$
We have,

$(5 a + 10) = (4 a + 8) + \text{Dropped Number}$.

Hence, the number dropped is $(5 a + 10) - (4 a + 8) = a + 2$.

Since $c = a + 2$, the answer is (C).

## (3) Comment(s)

Deep
()

just add 1 to 5 divide it 1/5....u wil get 3 which is 'c'.

Geetha
()

can we do in another method like

20% of the total sum

$=(5a+10)*(20/100)$

then also we are getting same answer $a+2$

Apoorv Jain
()

another method:-

assume numbers as 1,2,3,4,5.

sum = 15.

now what is the 20% of 15.... ans is 3.

so we can conclude that if 3 is remove then the sum will be decrease by 20%.

hence, 3 (or the 3rd number is the answer).