Question:medium

Aman purchased 8 mangoes, 6 oranges and 4 apples for a certain amount. With 35% less amount, Pavan could purchase 4 mangoes, 3 oranges and 3 apples. What percentage of the total amount did Aman spend on apples?

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Double Pavan's equation so the mango and orange terms match Aman's exactly, then subtract to isolate the apple price directly, without needing to know the mango or orange prices.
Updated On: Jul 21, 2026
  • 45%
  • 50%
  • 60%
  • 80%
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The Correct Option is D

Solution and Explanation

Step 1: Pick a convenient total and a free price.
Let Aman's total amount be \(T=100\). To get concrete numbers, choose the orange price \(o=0\) for a moment, just to solve the system; the final apple percentage will not actually depend on this choice, since the equations do not fix m and o separately.

Step 2: Write both equations with o = 0. \[ 8m+4p = 100 \] \[ 4m+3p = 65 \]

Step 3: Solve the two equations together.
From the first equation, \(m = \dfrac{100-4p}{8}\). Substituting into the second: \[ 4\left(\frac{100-4p}{8}\right)+3p = 65 \] \[ \frac{100-4p}{2}+3p = 65 \] Multiply through by 2: \[ 100-4p+6p = 130 \] \[ 2p = 30 \] \[ p = 15 \]

Step 4: Find m and check both equations.
\(m = \dfrac{100-4(15)}{8} = \dfrac{40}{8}=5\). Check: \(8(5)+4(15)=40+60=100\), correct. And \(4(5)+3(15)=20+45=65\), which is 35% less than 100, correct.

Step 5: Compute Aman's apple percentage.
Aman's apple spend is \(4p = 4\times15=60\), out of a total of 100, which is 60%.
Even though o was set to 0 just to get numbers, the apple percentage matches the algebraic elimination method exactly, confirming the price of oranges never actually affects the answer. \[ \boxed{60\%} \]
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