Question

A picture was bought at a certain sum, which was the price paid for its frame. Had the frame cost Rs 100 less and the picture Rs 75 more the price for the frame would have been only half of that of the picture. What is the price of the frame?

• A. 75
• B. 100
• C. 175
• D. 275

Answer 1

The Correct Option is D

Let the cost of the picture be Rs x and the cost of the frame be Rs y. According to the problem, we have the original equation as:
x = y
Now, adjusting the costs as per the conditions given, we have:

• The new cost of the frame = y - 100
• The new cost of the picture = x + 75
• According to the problem, the adjusted cost of the frame is half of that of the picture:
  y - 100 = 0.5 * (x + 75)

Using the initial condition x = y, we can substitute x with y in the second equation:
y - 100 = 0.5 * (y + 75)
Expanding and simplifying the equation:

• y - 100 = 0.5y + 37.5
• y - 0.5y = 37.5 + 100
• 0.5y = 137.5

Solving for y:
y = 275
Thus, the price of the frame is Rs 275.