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When the market price per kg of rice and wheat be in the ratio 3 : 2. The monthly expenses of a family towards rice and wheat are in the ratio 5 : 6. If the market price of rice and wheat becomes in the ratio of 4 : 3, what will be the ratio of expenses toward them? (the amount of rice and wheat consumed remains unchanged)
23 : 27
20 : 26
22 : 27
20 : 27
None of these
- The market price of rice and wheat is originally in the ratio 3:2.
- Monthly expenses for rice and wheat are in the ratio 5:6.
- When the price ratio changes to 4:3, expenses need to be recalculated.
- Assume the amount bought remains the same.
- If P is the price per kg and Q is the quantity:
- Original expense for rice = 3P * Q = 3PQ.
- Original expense for wheat = 2P * (Q / 3 * 6/5) = 4PQ.
- New expenses:
- New price for rice = 4P/3.
- New price for wheat = 3P/2.
- New expense ratio: (4P/3 * Q) / (3P/2 * (Q/3 * 6/5)).
- Calculate and simplify new ratio:
- Ratio = 20 : 27.
- Correct option is 20 : 27.
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