Question:easy

The sum of two numbers is 2490. If 6.5% of one number is equal to 8.5% of the other, the numbers are

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Equal products mean the numbers are inversely proportional to the percentages, so x : y = 8.5 : 6.5 = 17 : 13. Split 2490 into 30 parts. Also, only one option even adds to 2490.
Updated On: Jul 17, 2026
  • 1411 and 1079
  • 1412 and 1080
  • 1141 and 1709
  • 1214 and 1800
Show Solution

The Correct Option is A

Solution and Explanation

Step 1: Test the sum first, since it is the cheapest filter.
Every option must add up to 2490.
(A) $1411 + 1079 = 2490$. Passes.
(B) $1412 + 1080 = 2492$. Fails.
(C) $1141 + 1709 = 2850$. Fails.
(D) $1214 + 1800 = 3014$. Fails.
Only one option survives, so option (A) must be the answer. Still, it is worth deriving it properly.

Step 2: Derive the split from the ratio idea.
If $6.5\%$ of one number equals $8.5\%$ of the other, then the numbers are inversely proportional to those percentages.
A smaller percentage needs a bigger number to reach the same product, and the other way round.
So the numbers stand in the ratio $8.5 : 6.5$, which cleans up to $85 : 65$, then to $17 : 13$.

Step 3: Split 2490 in the ratio 17 to 13.
Total parts $= 17 + 13 = 30$.
One part $= \dfrac{2490}{30} = 83$.
Larger number $= 17 \times 83 = 1411$.
Smaller number $= 13 \times 83 = 1079$.

Step 4: Verify the percentage condition exactly.
$6.5\%$ of $1411$: $\dfrac{13}{200} \times 1411 = \dfrac{18343}{200} = 91.715$.
$8.5\%$ of $1079$: $\dfrac{17}{200} \times 1079 = \dfrac{18343}{200} = 91.715$.
Identical, so the split is right.

Step 5: One point to remember.
$1411 = 17 \times 83$ and $1079 = 13 \times 83$ share the factor 83. Whenever a ratio question has a clean total like 2490, look for a common factor, since 2490 = 30 times 83.

Final Answer:
The numbers are 1411 and 1079, option (A). \[ \boxed{1411 \text{ and } 1079} \]
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