Question

A starts a business with Rs.5000 and B joins the business 5 months later with an investment of Rs.6000. After a year they earn a profit of Rs. 34000 . Find the shares of A and B in the profit amount depending on their individual investment
a.Rs. 20000 , Rs.14000
b.Rs 16000 , Rs 16000
c.Rs.14,000 ,Rs.20000

Answer 1

Hint: We are given the investments of A and B with which we can calculate the effective price contributed by them . Effective price is given by multiplying their investment amount into the number of months contributed and we need to find the ratio of their effective price and with that ratio we get the total number of parts by which the profit has to be divided and the numbers of parts belonging to A and B.

Complete step-by-step answer:
As A starts the business with Rs.5000
The effective price contributed by A for a year is given by
$ \Rightarrow 5000*12 = 60000$
We are given that B invests 6000 only after 5 months
Therefore he has contributed only for 7 months in that particular year
Hence , the effective price contributed by B for a year is given by
$ \Rightarrow 6000*7 = 42000$
The ratio of the contribution of A and B be
$ \Rightarrow \dfrac{A}{B} = \dfrac{{60000}}{{42000}} = \dfrac{{10}}{7}$
Therefore the ratio is 10:7
The profit for the year is Rs.34000
With the ratio we can see that the profit is divided into 17 parts out of which 10 parts belongs to A and remaining 7 parts belong to B
Therefore,
The profit share of A $ = \dfrac{{10}}{{17}}*34000$
 $
   = 10*2000 \\
   = Rs.20000 \\
$
 The profit share of A $ = \dfrac{7}{{17}}*34000$
   $
   = 7*2000 \\
   = Rs.14000 \\
$
Hence we get that the share of A is Rs.20000 and B is Rs.14000
The correct option is a .

Note: Many students tend to think that they may get equal shares or B gets the largest share as he invests 6000 but only when we find the effective price we get the correct amount invested .
A ratio between two or more quantities is a way of measuring their sizes compared to each other