33. If 20% of \(x + y\) is equal to 50% of \(x – y\), what is \(x : y\)?
Answer: (A) 7 : 3
Given: \(0.2(x + y) = 0.5(x – y)\)
Multiply both sides by 10: \(2(x + y) = 5(x – y)\)
Expanding: \(2x + 2y = 5x – 5y\)
Rearranging: \(2x – 5x + 2y + 5y = 0 \Rightarrow -3x + 7y = 0\)
So, \(3x = 7y \Rightarrow x/y = 7/3\)
Hence, the ratio \(x : y\) is 7 : 3, matching option (A).
Multiply both sides by 10: \(2(x + y) = 5(x – y)\)
Expanding: \(2x + 2y = 5x – 5y\)
Rearranging: \(2x – 5x + 2y + 5y = 0 \Rightarrow -3x + 7y = 0\)
So, \(3x = 7y \Rightarrow x/y = 7/3\)
Hence, the ratio \(x : y\) is 7 : 3, matching option (A).
34. While selling a watch a shopkeeper gives a discount of 5% on its marked price. If he gives a discount of 10%, then he earns ₹25 less as profit. What is the marked price of the watch?
Answer: (B) ₹500
Let the marked price be \(M\).
Selling price at 5% discount = \(0.95M\)
Selling price at 10% discount = \(0.90M\)
Difference in profit = \(0.95M – 0.90M = ₹25\)
So, \(0.05M = 25 \Rightarrow M = ₹500\)
Therefore, the marked price is ₹500, which matches option (B).
Selling price at 5% discount = \(0.95M\)
Selling price at 10% discount = \(0.90M\)
Difference in profit = \(0.95M – 0.90M = ₹25\)
So, \(0.05M = 25 \Rightarrow M = ₹500\)
Therefore, the marked price is ₹500, which matches option (B).