Question

P is six times as large as Q. By what per cent is Q less than P?

• A. 16 \(\frac{2}{3}\)%
• B. 60%
• C. 83 \(\frac{1}{3}\)%
• D. 90%

Answer 1

The Correct Option is C

P is six times as large as Q. Let's denote P as 6Q.

We need to calculate by what percent Q is less than P.

First, find the difference between P and Q: \(P - Q = 6Q - Q = 5Q\).

The percent by which Q is less than P is given by the formula:

\[\text{Percent less} = \left(\frac{\text{Difference}}{P}\right) \times 100\]

Substitute the values:

\[\text{Percent less} = \left(\frac{5Q}{6Q}\right) \times 100\]

Simplify the expression:

\[\text{Percent less} = \frac{5}{6} \times 100 = 83.33\%\]

Therefore, Q is 83 \(\frac{1}{3}\)% less than P.