Question

The sum of two numbers is 4000. 10% of one number is $ 6\dfrac{2}{3}\% $ of the other. The difference of the number is
A.600
B.800
C.1025
D.1175

Answer 1

Hint: First of all, let the two numbers be x and y. Now, form an equation with these variables. Now, we are given that 10% of one number (x) is equal to the $ 6\dfrac{2}{3}\% $ of the other number (y). So, $ \dfrac{{10}}{{100}} \times x $ will be equal to $ \dfrac{{6 \times 3 + 2}}{3} \times \dfrac{1}{{100}} \times y $ . Now, we have two linear equations and solving them we will get the two numbers.

Complete step-by-step answer:
In this question, we are given that the sum of two numbers is 4000 and 10% of one number is equal to $ 6\dfrac{2}{3}\% $ of other numbers. We need to find the difference between these two numbers.
Let these two numbers be equal to x and y.
Therefore, we get equation
 $ \Rightarrow x + y = 4000 $ - - - - - - - - - (1)
Now, we are given that 10% of one number (x) is equal to $ 6\dfrac{2}{3}\% $ of other numbers (y). Therefore, we get
 $ \Rightarrow $ 10% of x $ = \dfrac{{10}}{{100}} \times x $
 $ \Rightarrow $ $ 6\dfrac{2}{3}\% $ of y $ = \dfrac{{6 \times 3 + 2}}{3} \times \dfrac{1}{{100}} \times y $
  $ = \dfrac{{20}}{{300}} \times y $
Now, they both are equal. So, therefore, we get
 $
   \Rightarrow \dfrac{{10}}{{100}} \times x = \dfrac{{20}}{{300}} \times y \\
   \Rightarrow x = \dfrac{2}{3} \times y \;
  $
Substitute these values in equation (1), we get
 $
   \Rightarrow \dfrac{{2y}}{3} + y = 4000 \\
   \Rightarrow \dfrac{{2y + 3y}}{3} = 4000 \\
   \Rightarrow 5y = 12000 \\
   \Rightarrow y = 2400 \;
  $
Now,
 $ \Rightarrow x = \dfrac{2}{3} \times y $
Therefore,
 $
   \Rightarrow x = \dfrac{2}{3} \times 2400 \\
   \Rightarrow x = 1600 \;
  $
Hence, the two numbers are 1600 and 2400.
Now, we need to find the difference between these two numbers. Therefore,
 $ \Rightarrow $ Difference of numbers $ = 2400 - 1600 = 800 $ .
Hence, our answer is option B.
So, the correct answer is “Option B”.

Note: Here, note that we also have to convert $ 6\dfrac{2}{3}\% $ which is a mixed number while converting it into fraction form. We can cross verify our answer by finding 10% and $ 6\dfrac{2}{3}\% $ of 2400 and 1600 respectively.
 $ \Rightarrow $ 10% of 1600 $ = \dfrac{{10}}{{100}} \times 1600 = 160 $
 $ \Rightarrow $ $ 6\dfrac{2}{3}\% $ of 1800 $ = \dfrac{{6 \times 3 + 2}}{3} \times \dfrac{1}{{100}} \times 2400 $
 $ = 160 $
Hence, 10% of 1600 $ = $ $ 6\dfrac{2}{3}\% $ of 1800.