Question

If $ \dfrac{3}{5} $ of a number exceeds it’s $ \dfrac{2}{7} $ by $ 44 $ , find the number.

Answer 1

Hint: In this we first let a number be as ‘x’ then finding its three fifth and two seventh and as it is given that three fifth of a number is greater by $ 44 $ . Then finding the difference of two numbers obtained in terms of ‘x’ and equating to $ 44 $ and then solving the equation so formed to find value of ‘x’ and hence required solution of given problem.

Complete step-by-step answer:
For this let the number is ‘x’
Then we will first calculate $ \dfrac{3}{5} $ of the number.
Therefore, we have $ \dfrac{3}{5}x................(i) $
Now, calculating $ \dfrac{2}{7} $ of ‘x’
Therefore, we will have $ \dfrac{2}{7}x.................(ii) $
Since, it’s given that $ \dfrac{3}{5} $ of a number exceeds its $ \dfrac{2}{7} $ or we can say that $ \dfrac{3}{5}x $ is greater than $ \dfrac{2}{7}x $ by $ 44 $ .
Hence, from above we have,
 $ \dfrac{3}{5}x - \dfrac{2}{7}x = 44 $
Simplifying the above equation by taking its LCM.
 $ \dfrac{{21x - 10x}}{{35}} = 44 $
On cross multiplying we have,
 $
  21x - 10x = 35 \times 44 \\
   \Rightarrow 11x = 1540 \\
   \Rightarrow x = \dfrac{{1540}}{{11}} \\
   \Rightarrow x = 140 \;
  $
Therefore, from above we see that required number is $ 140. $
So, the correct answer is “140”.

Note: For this type of problem in which numbers are depending upon other numbers. Therefore, first considering a number as ‘x’ then finding three fifth and two seventh of ‘x’ and then adding $ 44 $ to two seventh so that it will be equal to three fifth of number ‘x’ and solving the equation so formed to find value of ‘x’ or required solution of given problem.