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Select the correct answerIf the price of gold increases by 40% find the percentage decrease in the quantity of gold purchased by a man who can afford only a 20% increase in expenditure in the purchase of gold?Options14.29%16.67%20%33.33%

Question

Select the correct answerIf the price of gold increases by 40% find the percentage decrease in the quantity of gold purchased by a man who can afford only a 20% increase in expenditure in the purchase of gold?Options14.29%16.67%20%33.33%

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Solution

To solve this problem, we need to understand that the man's expenditure is made up of the price of gold and the quantity he purchases. If the price of gold increases by 40% but he can only afford a 20% increase in expenditure, he will have to buy less gold to stay within his budget.

Let's denote the initial price of gold as P and the initial quantity of gold he purchases as Q. His initial expenditure is therefore P*Q.

After the price increase, the price of gold is now 1.4P (which is a 40% increase). Let's denote the new quantity of gold he purchases as Q1. His expenditure is now 1.4P*Q1.

However, he can only afford a 20% increase in expenditure, so 1.4PQ1 = 1.2PQ.

Solving for Q1 gives us Q1 = (1.2/1.4)Q = 0.857Q.

This means the quantity of gold he purchases has decreased to 85.7% of the original quantity. To find the percentage decrease, we subtract this from 100%, giving us 100% - 85.7% = 14.3%.

So, the correct answer is 14.29%.

This problem has been solved

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