Question

Arun, Kamal and Vinay invested Rs. 8000, Rs. 4000 and Rs. 8000 respectively in a business. Arun left after six months. If after eight months, there was a gain of Rs. 4005, then what will be the share of Kamal?
A. Rs. 890
B. Rs. 1335
C. Rs. 1602
D. Rs. 1780

Answer 1

Hint: Firstly we will find the total amount invested separately by multiplying their respective investment months. Later on form the ratios between their respective investments.
A ratio can be written in three different ways and all are read as "the ratio of x to y"
\[\begin{array}{*{20}{l}}
  {x\;to\;y} \\
  {x:y} \\
  {\dfrac{x}{y}}
\end{array}\]

Complete step-by-step answer:
First let us calculate the invested money of each person.
Arun money invested: -
Money Invested = Rs. 8000
Months the money invested = 6
So, Arun money total invested =$8000{\rm X}6 = Rs.\;48000$ ………………….(1)
Kamal money invested: -
Money Invested = Rs. 4000
Months the money invested = 8
So, Kamal money total invested =$4000{\rm X}8 = Rs.\;32000$………………….(2)
Vinay money invested: -
Money Invested = Rs. 8000
Months the money invested = 8
So, Vinay money total invested =$8000{\rm X}8 = Rs.\;64000$………………….(3)
By using equations (1), (2) and (3)
$
  Ratio = Arun:Kamal:Vinay \\
   \Rightarrow Ratio = 48000:32000:64000 \\
   \Rightarrow Ratio = 48:32:64 \\
   \Rightarrow Ratio = 3:2:4 \\
 $
Total shares will be = 3+2+4 =9
Total profit = Rs. 4005
Kamal Share is =2
So, the Kamal profit will be =\[\dfrac{2}{9}{\rm X}4005 = 2{\rm X}445 = Rs.890\]

So, the correct answer is “Option A”.

Note: A ratio is how many times bigger one thing is than another. It's a number you multiply by to get one thing from another. But remember, when you find the ratio of two quantities, they must be in the same units.