Question

Fifty percent of a number \(P\) is \(12\) more than \(60\) percent of a number Q. If \(P+Q=156\), then what would be the value of \(75\) percent of \(P\)?

• A. 48
• B. 72
• C. 42
• D. 96

Answer 1

The Correct Option is B

We are given the following information:

• 50% of a number P is 12 more than 60% of a number Q, i.e.,  
  $\frac{50}{100}P = \frac{60}{100}Q + 12$
• P + Q = 156

First, simplify the given equation:

$\frac{1}{2}P = \frac{3}{5}Q + 12$

Multiply the entire equation by 10 to eliminate fractions:

5P = 6Q + 120

Thus, we have our first equation:

Equation 1: 5P = 6Q + 120

Now, from the second condition P + Q = 156, we can express P as:

Equation 2: P = 156 - Q

Substitute Equation 2 into Equation 1:

5(156 - Q) = 6Q + 120

Simplify:

Solve for Q:

780 - 5Q = 6Q + 120

780 - 120 = 6Q + 5Q

660 = 11Q

$Q = \frac{660}{11} = 60$

Now, substitute Q = 60 back into Equation 2 to find P:

P = 156 - 60 = 96

Finally, find 75% of P:

75% of P = $\frac{75}{100} \times 96 = 72$

Thus, the correct answer is (b) 72.