A vendor has 374 fruits in total, made up of apples, mangoes and oranges. Apples and mangoes are present in the ratio 5:2. She sells 150 apples, 52 mangoes and half of the oranges. The numbers of unsold apples and unsold oranges are then in the ratio 3:2. Find the total number of fruits remaining unsold.
Answer and solution
Correct answer: 132
Solution
Answer: 132
1. Set apples=5k and mangoes=2k. The original oranges are 374−7k.
2. After selling, apples=5k−150, mangoes=2k−52, oranges=(374−7k)/2.
3. Apply the remaining ratio: (5k−150)/[(374−7k)/2]=3/2. Thus 4(5k−150)=3(374−7k).
4. Solve 20k−600=1122−21k: k=42. Original stock is 210,84,80.
5. Remaining stock is 60,32,40. Total=132. Check 60:40=3:2.
Why this method works:
The original apples: mangoes ratio introduces one shared multiplier, reducing three stock variables to one after using the total. The unsold ratio must be applied only after subtracting the specified sales; it does not describe the original fruit mix.
Independent check and common trap:
With k=42, original quantities 210+84+80=374. Sales are 150+52+40=242, leaving 374−242=132. This independent total check agrees with 60+32+40 and the remaining apple: orange ratio 3:2.
Apply: Use one multiplier k: apples=5k, mangoes=2k. Combine the total and the UNSOLD ratio; do not apply 3:2 to the original stock.
Check: With k=42, original quantities 210+84+80=374. Sales are 150+52+40=242, leaving 374−242=132. This independent total check agrees with 60+32+40 and the remaining apple: orange ratio 3:2.
1. Set apples=5k and mangoes=2k. The original oranges are 374−7k.
2. After selling, apples=5k−150, mangoes=2k−52, oranges=(374−7k)/2.
3. Apply the remaining ratio: (5k−150)/[(374−7k)/2]=3/2. Thus 4(5k−150)=3(374−7k).
4. Solve 20k−600=1122−21k: k=42. Original stock is 210,84,80.
5. Remaining stock is 60,32,40. Total=132. Check 60:40=3:2.
Why this method works:
The original apples: mangoes ratio introduces one shared multiplier, reducing three stock variables to one after using the total. The unsold ratio must be applied only after subtracting the specified sales; it does not describe the original fruit mix.
Independent check and common trap:
With k=42, original quantities 210+84+80=374. Sales are 150+52+40=242, leaving 374−242=132. This independent total check agrees with 60+32+40 and the remaining apple: orange ratio 3:2.
G Strategy shortcut
Spot: Ratio and Proportion.Apply: Use one multiplier k: apples=5k, mangoes=2k. Combine the total and the UNSOLD ratio; do not apply 3:2 to the original stock.
Check: With k=42, original quantities 210+84+80=374. Sales are 150+52+40=242, leaving 374−242=132. This independent total check agrees with 60+32+40 and the remaining apple: orange ratio 3:2.
G Strategy: Spot: Ratio and Proportion. Apply: Use one multiplier k: apples=5k, mangoes=2k. Combine the total and the UNSOLD ratio; do not apply 3:2 to the original stock. Check: With k=42, original quantities 210+84+80=374. Sales are 150+52+40=242, leaving 374−242=132. This independent total check agrees with 60+32+40 and the remaining apple: orange ratio 3:2.