Question

Which one of the following is the same as $ 30\% {\rm{ of }}40\% {\rm{ of 560}} $ ?
(A) $ 60\% {\rm{ of }}40\% {\rm{ of 280}} $
(B) $ 15\% {\rm{ of 80\% of 280}} $
(C) $ {\rm{30\% of 40\% of 280}} $
(D) $ {\rm{15\% of 80\% of 140}} $

Answer 1

Hint: This is a multiplication between a number and a percent. A percent itself represents a fraction whose value is $ \dfrac{1}{{100}} $ times the number. For example, the value of $ 10\% $ is same as the value of $ 10 \times \dfrac{1}{{100}}{\rm{ or }}\dfrac{{10}}{{100}} $ .

Complete step-by-step answer:
The given value that we have to compare with the options given is –
 $ 30\% {\rm{ of }}40\% {\rm{ of 560}} $
Now solving this we get-
 $ \begin{array}{c}
30\% {\rm{ of }}40\% {\rm{ of 560 = }}\dfrac{{30}}{{100}} \times \dfrac{{40}}{{100}} \times 560\\
 = \dfrac{{672000}}{{10000}}\\
 = 67.2
\end{array} $
So, the value of $ 30\% {\rm{ of }}40\% {\rm{ of 560}} $ is $ 67.2 $ .
Now we have to find the value for each option given and then compare with the value we have calculated. If the value of any of the options given matches with the value, we have calculated then that is our answer.
So, considering first option-
Option (A) $ 60\% {\rm{ of }}40\% {\rm{ of 280}} $
Solving this we get,
 $ \begin{array}{c}
60\% {\rm{ of }}40\% {\rm{ of 280 = }}\dfrac{{60}}{{100}} \times \dfrac{{40}}{{100}} \times 280\\
 = \dfrac{{672000}}{{10000}}\\
 = 67.2
\end{array} $
So, the value of $ 60\% {\rm{ of }}40\% {\rm{ of 280}} $ is $ 67.2 $ .

Similarly, considering second option-
Option (B) $ 15\% {\rm{ of 80\% of 280}} $
Solving this we get,
 $ \begin{array}{c}
15\% {\rm{ of 80\% of 280 = }}\dfrac{{15}}{{100}} \times \dfrac{{80}}{{100}} \times 280\\
 = \dfrac{{336000}}{{10000}}\\
 = 33.6
\end{array} $
So, the value of $ 15\% {\rm{ of 80\% of 280}} $ is $ 33.6 $ .

Considering the third option-
Option (C) $ {\rm{30\% of 40\% of 280}} $
Solving this we get,
 $ \begin{array}{c}
{\rm{30\% of 40\% of 280 = }}\dfrac{{30}}{{100}} \times \dfrac{{40}}{{100}} \times 280\\
 = \dfrac{{336000}}{{10000}}\\
 = 33.6
\end{array} $
So, the value of $ {\rm{30\% of 40\% of 280}} $ is $ 33.6 $ .
And, considering the fourth option-

Option (D) $ {\rm{15\% of 80\% of 140}} $
Solving this we get,
\[\begin{array}{c}
{\rm{15\% of 80\% of 140 = }}\dfrac{{15}}{{100}} \times \dfrac{{80}}{{100}} \times 140\\
 = \dfrac{{168000}}{{10000}}\\
 = 16.8
\end{array}\]
So, the value of $ {\rm{15\% of 80\% of 140}} $ is $ 16.8 $ .
Now, comparing the values of the options we have calculated to the value of $ 30\% {\rm{ of }}40\% {\rm{ of 560}} $ , we see that the values are same for Option (A).
Therefore, the correct answer is (A) $ 60\% {\rm{ of }}40\% {\rm{ of 280}} $ .

Note: The method of multiplication of any percent number is the same as any other number, we just have to convert the result into the required form. The conversion formula for percent is given below-
From percentage to fraction:
 $ N\% = N \times \dfrac{1}{{100}} $