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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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
Question : Arrange the given ratios in descending order 15 : 7, 5 : 11, and 21 : 77.
Option 1: 21 : 77 > 5 : 11 > 15 : 7
Option 2: 15 : 7 > 5 : 11 > 21 : 77
Option 3: 15 : 7 > 21 : 77 > 5 : 11
Option 4: 5 : 11 > 15 : 7 > 21 : 77
Question : If the sum of two numbers is 60 and their HCF and LCM are 5 and 60, respectively, then the sum of the reciprocals of the numbers will be:
Option 1: $\frac{1}{11}$
Option 2: $\frac{1}{6}$
Option 3: $\frac{1}{4}$
Option 4: $\frac{1}{5}$
Question : Directions: When a number is added to its next number and another number that is four times its next number, the sum of these three numbers is 95. Find the number.
Option 1: 16
Option 2: 14
Option 3: 17
Question : The ratio of two numbers is 3 : 5. If eight is added to the first, and seven to the second, then the ratio becomes 2 : 3. What will the ratio become if six is added to each?
Option 1: 9 : 14
Option 2: 5 : 7
Option 3: 5 : 9
Option 4: 7 : 9
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