Question

M and N invested in a business in which M invests Rs250 more than N.N invested for 6 months while M invested for 4 months. If M gets Rs 200 more than out of a total profit of Rs.1,000, then what is the total amount invested in the business.

Answer 1

Hint- Take the unknown value as x and try to express the data given in the form of an equation and try to find out the solution.

Complete step-by-step answer:
Given that M invested Rs 250 more than N
So, let us consider the investment made by N=Rs. x
Then, the investment made by M would be x+250
M invests for a total of 4 months,
N invests for a total of 6 months,
So, the total investment by M would be (x+250)$ \times 4$=4x+1000 and
The total investment made by N would be 6x
Ratio of both of their profits (4x+1000):6x
Also, given that the total profit by both of them=Rs.1,000
Given that M gets a profit of Rs.200 more than N
According to the problem , if we try to represent the given data in the form of equation , we get
$\dfrac{{Ratio{\text{ of profit of M - N}}}}{{{\text{Sum of the ratio of the ratio of the profits}}}} \times Total{\text{ Profit = 200}}$
 From this, we can further write this as
$\dfrac{{1000 - 2x}}{{1000 + 10x}} \times 5 = 1$
5000-10x=1000+10x
$ \Rightarrow 4000 = 20x$
From this, we get x=Rs.200
Total investment would be investment of M +investment of N
=4x+1000+6x
=4(200)+1000+6(200)
=800+1000+1200
=Rs.3,000
So, the total amount invested in the business by both M and N is Rs.3000

Note: Take care not to just find out the value of x and stop there , we have to find out the value of the total investment , so we have to find out the value of 4x+1000 and 6x and add them up which will give us the total investment.