Question

A, B and C enter into a partnership. They invest Rs. 40000, Rs. 80000 and Rs. 120000 respectively. At the end of the first year, B withdraws Rs. 40000, while at the end of the second year, C withdraws Rs. 80000. In what ratio will the profit be shared at the end of 3 years?
A. 2 : 3 : 5
B. 3 : 4 : 7
C. 4 : 5 :9
D. None of these

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.
A money invested: -
Money Invested = Rs. 40000
Months the money invested = 3 years
So, A money total invested =$40000 {\rm X} 3 = Rs.\;120000$ ………………….(1)
B money invested: -
Money Invested = Rs. 80000
Months the money invested = 1 year
After 1 year B withdraws Rs. 40000
So for the money invested for next 2 years = Rs. 40000
So, B money total invested =$80000 {\rm X} 1 + 40000 {\rm X} 2 = Rs.\;160000$………………….(2)
C money invested: -
Money Invested = Rs. 120000
Months the money invested = 2 years
After 2 years C withdraws Rs. 80000
So for the money invested for next 1 year = Rs. 40000
So, C money total invested =$120000 {\rm X} 2 + 40000 {\rm X} 1 = Rs.\;280000$………………….(3)
By using equations (1), (2) and (3)
$
  Ratio = A:B:C \\
   \Rightarrow Ratio = 120000:160000:280000 \\
   \Rightarrow Ratio = 12:16:28 \\
   \Rightarrow Ratio = 3:4:7 \\
 $

So, the correct answer is “Option B”.

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.