If income of R is 30% more than the income of Q and the income of Q is 20% more than the income of P, then the income of R is how much percent more than the income of P?

Options

A. a)50
B. b)10
C. c)56
D. d)55

Answer

To solve the problem step by step, let's denote the incomes of P, Q, and R as follows:

- Let the income of P be \( P \).
- The income of Q is 20% more than the income of P, so:
\[ Q = P + 0.2P = 1.2P \]

- The income of R is 30% more than the income of Q, so:
\[ R = Q + 0.3Q = 1.3Q \]

Now, substituting the value of Q from the previous step into the equation for R:
\[ R = 1.3 \times (1.2P) = 1.56P \]

Now we need to find out how much percent more the income of R is than the income of P. To do this, we can use the formula for percentage increase:
\[ \text{Percentage Increase} = \left( \frac{R - P}{P} \right) \times 100 \]

Substituting the value of R:
\[ \text{Percentage Increase} = \left( \frac{1.56P - P}{P} \right) \times 100 \]
\[ = \left( \frac{0.56P}{P} \right) \times 100 \]
\[ = 0.56 \times 100 = 56\% \]

Thus, the income of R is 56% more than the income of P.