The sum of two numbers is 480. If the bigger number is decreased by 2% and the…
2023
The sum of two numbers is 480. If the bigger number is decreased by 2% and the smaller number is increased by 10%, then the numbers obtained are equal. The larger number is approximately
Answer: B. 3300/13 — ConceptWhen two changed quantities become equal, express each percentage change as a multiplier and equate the resulting values. A decrease of p% multiplies a…
- A.
3320/13
- B.
3300/13
- C.
3120/13
- D.
More than one of the above
- E.
None of the above
Attempted by 22 students.
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Correct answer: B
Concept
When two changed quantities become equal, express each percentage change as a multiplier and equate the resulting values.
A decrease of p% multiplies a quantity by (100-p)/100, while an increase of p% multiplies it by (100+p)/100. Combine this relation with the given sum.
Application
Let L be the larger number and S be the smaller number. Then L + S = 480.
After the stated changes, 0.98L = 1.10S.
Removing decimals gives 98L = 110S, so 49L = 55S and L:S = 55:49.
The total 480 corresponds to 55 + 49 = 104 ratio-parts, so L = 480 × 55/104 = 3300/13 ≈ 253.85.
Cross-check
Using S = 480 × 49/104 = 2940/13, we get 0.98L = 3234/13 and 1.10S = 3234/13; the changed values are equal.
Result
Therefore, the larger number is 3300/13, approximately 253.85.