If 35 percent of a number is added to another number then the first number…
2024
If 35 percent of a number is added to another number then the first number becomes 98 percent of itself. What will be the ratio of first and second numbers?
- A.
101 : 63
- B.
100 : 67
- C.
105 : 63
- D.
100 : 63
Attempted by 8 students.
Show answer & explanation
Correct answer: D
Step-by-Step Solution
To find the ratio of the first number to the second number, we can set up an algebraic equation based on the given conditions.
Define the variables:
Let the first number be x and the second number be y.
Translate the problem into an equation:
"35 percent of a number (x) is added to another number (y) then the first number (x) becomes 98 percent of itself".
0.35x + y = 0.98x
Solve for y in terms of x:
y = 0.98x - 0.35x
y = 0.63x
Find the ratio x : y:
Divide both sides by y, then by 0.63:
x / y = 1 / 0.63
To convert the decimal to a fraction, multiply both numerator and denominator by 100:
x / y = 100 / 63
The ratio x : y is 100 : 63.