Question : A boy added all-natural numbers from 1 to 20. However, he added one number twice, due to which the sum became 215. What is the number which he added twice?
Option 1: 5
Option 2: 7
Option 3: 11
Option 4: 15
Correct Answer: 5
Solution :
Let the number added twice be $x$.
The sum of all $n$ natural numbers = $\frac{n(n + 1)}{2}$
The sum of all natural numbers from 1 to 20 = $\frac{20(20 + 1)}{2}$ = $\frac{21 × 20}{2}$ = 210
According to the question,
⇒ 210 + $x$ = 215
⇒ $x$ = 5
Hence, the correct answer is 5.
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