Question

X and Y invest Rs. 21000 and Rs. 17500 and respectively in a business. At the end of the year, they make a profit of Rs.26400 . What is the share of X in the profit?

Answer 1

Hint: To solve this question, first we should understand that the given question belongs to the topic ratio and proportion. So, first we will find the ratio of X and Y and the sum of their ratios respectively. Then only we can conclude the share of both the investments.

Complete step by step solution:
The investment of X is Rs. 21000 in a business.
The investment of Y is Rs. 17500 in a business.
Therefore, the investment ratio of X and Y is:
 $
  X:Y \\
   = 21500:17500 \\
   = 6:5 \;
  $
And, they make a profit of Rs.26400.
\[X:Y = 6:5\]
So, the share of X in the above profit is:
 $ Share\,\,of\,X = \dfrac{{Ratio\,of\,X}}{{Sum\,of\,ratios\,of\,X\,\& \,Y}} \times \Pr ofit $
 $ \therefore Share\,\,of\,X = \dfrac{6}{{11}} \times 26400 $
 $ Share\,of\,X = 14400 $
Hence, the share of X in the given profit is $ Rs.14400 $ .
So, the correct answer is “ $ Rs.14400 $ ”.

Note: We can also find the share of X by assuming the sum of ratios as parts. That means if the profit amount Rs.26400 is divided into 11 parts in which 6 parts go to X and 5 parts go to Y
So, \[Share\,of\,X = \dfrac{{26400}}{{11}} \times 6 = 14400\] .
And, $ Share\,of\,X = 26400 - 14400 = 12000 $ .