If 427.27% of a number is added to one-third of itself, then it becomes 12,920. Find 20% of the original number.

(a) 561
(b) 374

The original number is approximately 2805.3, and 20% of this number is 561. The chosen answer is (a) 561.
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Answered by Anonymous | 2025-07-11

To solve this problem, let's define the original number as x .
According to the problem statement, 427.27% of the number is added to one-third of itself, and the result is 12,920.

Convert percentages to decimals and fractions:
427.27% is equal to 100 427.27 ​ = 4.2727 .

Translate the statement into an equation:
"If 427.27% of a number is added to one-third of itself, then it becomes 12,920" can be translated into the equation:
4.2727 x + 3 1 ​ x = 12 , 920

Combine the terms:
4.2727 x + 3 1 ​ x is the same as 4.2727 x + 0.3333 x .
Combine these terms:
( 4.2727 + 0.3333 ) x = 12 , 920
4.606 x = 12 , 920

Solve for x :
Divide both sides of the equation by 4.606 to find x :
x = 4.606 12 , 920 ​ ≈ 2 , 805

Find 20% of the original number:
20% of x is calculated as follows:
0.20 × 2 , 805 = 561


Therefore, 20% of the original number is 561.
Thus, the correct multiple choice option is (a) 561 .

Answered by MasonWilliamTurner | 2025-07-21