A person had to multiply two numbers. Instead of multiplying by 35, he…
2026
A person had to multiply two numbers. Instead of multiplying by 35, he multiplied by 53 and the product went up by 540. What was the raised product?
- A.
1908
- B.
1467
- C.
1590
- D.
1123
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Concept: When the same number is multiplied by two different multipliers, the difference between the two resulting products equals that number multiplied by the difference between the multipliers. In symbols, if the unknown number is x and the multipliers are m1 and m2, the difference between the products is (m1 − m2) × x.
Let the unknown number be x.
The intended product was 35 × x, but the product actually obtained was 53 × x.
The increase in the product = 53x − 35x = 18x.
This increase is given as 540, so 18x = 540.
Solving for x: x = 540 ÷ 18 = 30.
The raised (actual) product = 53 × x = 53 × 30 = 1590.
Cross-check: The originally intended product would have been 35 × 30 = 1050. Subtracting this from the raised product, 1590 − 1050 = 540, which matches the given increase — confirming that 1590 is correct.