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When one-fifth of a number is increased by 25, the result is 45. Find the sum of the digits of the original number.
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Subtract 25 from 45 to get 20, then multiply by 5 immediately to get 100. The sum of digits of 100 is 1+0+0 = 1.
One-fifth of a number x is increased by 25 to result in 45.
5xтАЛ+25=45
Subtract 25 from 45 to get 20, then multiply by 5 immediately to get 100. The sum of digits of 100 is 1+0+0 = 1.
Many students mistake the 'sum of digits' requirement and mistakenly choose the number 100 itself instead of calculating 1+0+0.
Formulating the equation
Let the number be x. According to the problem, one-fifth of x increased by 25 is 45.
5xтАЛ+25=45
Solving for x
Subtract 25 from both sides: 5xтАЛ=45тИТ25. This simplifies to 5xтАЛ=20.
x=20├Ч5=100
Calculating sum of digits
The original number is 100. The sum of its digits is 1+0+0.
1+0+0=1
A is correct because the number is 100 and the sum of its digits 1+0+0 equals 1.
This type of algebraic manipulation is fundamental for solving word problems in quantitative aptitude exams, often appearing in mixture or age-related problems.