If 35% of a number is 416 more than 27% of the same number, then the n

If 35% of a number is 416 more than 27% of the same number, then the number is

5200
2600
3900
3328
This question was previously asked in
UPSC CAPF – 2021
The number is 5200.
Translate the word problem into an algebraic equation involving percentages of an unknown number.
Let the number be N.
35% of the number = 0.35 * N
27% of the number = 0.27 * N
The problem states that 35% of the number is 416 more than 27% of the same number.
So, 0.35N = 0.27N + 416
Subtract 0.27N from both sides:
0.35N – 0.27N = 416
0.08N = 416
To find N, divide 416 by 0.08:
N = 416 / 0.08
N = 416 / (8/100)
N = 416 * (100/8)
N = (416/8) * 100
N = 52 * 100
N = 5200
The number is 5200.
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