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When one-third of a number is increased by 55, the result is 83. Find the sum of the digits of the original number.
13
14
12
9
12
Subtract 55 from 83 to get 28, then multiply by 3 to find the number (84). Sum of digits: 8 + 4 = 12.
One-third of a number is increased by 55 to result in 83.
3xтАЛ+55=83
Subtract 55 from 83 to get 28, then multiply by 3 to find the number (84). Sum of digits: 8 + 4 = 12.
Students often add 55 to the number instead of subtracting it from the result, or forget to perform the final step of summing the digits.
Define the Variable
Let the original number be x. According to the problem, one-third of this number is 3xтАЛ.
x
Set up the Equation
Based on the given condition that adding 55 gives 83, we form the linear equation.
3xтАЛ+55=83
Solve for x
Subtract 55 from both sides: 3xтАЛ=83тИТ55=28. Then, multiply by 3 to get x=28├Ч3=84.
x=84
Calculate Sum of Digits
The original number is 84. The sum of its digits is 8+4=12.
8+4=12
C is correct because the original number is 84 and the sum of its digits 8 + 4 equals 12.
This type of word problem frequently appears in Quantitative Aptitude sections. Always identify the unknown variable first and ensure you read the final requirement (sum of digits vs the number itself) carefully to avoid silly errors.
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