Question : A boy added all natural numbers from 1 to 12, but he added one number twice, due to which the sum became 80. What is the number that he added twice?
Option 1: 3
Option 2: 2
Option 3: 7
Option 4: 8
Correct Answer: 2
Solution :
Sum of the first $n$ natural numbers = $\frac{n(n + 1)}{2}$
Sum of the first 12 natural numbers = $\frac{12(12 + 1)}{2}$ = $\frac{12\times 13}{2}$ = 78
A number is added twice so that the sum becomes 80.
The number added twice is (80 – 78) = 2
Hence, the correct answer is 2.
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