Question

A’s money is to B’s money is 4:5 and B’s money is to C’s money is 2:3. If A has Rs.800, C has
A. Rs.1000
B. Rs.1200
C. Rs.1500
D. Rs.2000

Answer 1

Hint: This problem deals with ratios and proportions. Ratio is a way to compare two quantities by using division. A proportion on the other hand is an equation that says that two ratios are equivalent. If one number in proportion is unknown you can find that number by solving the proportion. Similarly in this case the ratio of money of A and B is given where the money that B has is unknown. So finding the unknown money through the ratio and proportions.

Complete step-by-step answer:
Given that the ratio of the money between A and B, which is given by 4:5
Also given the ratio of the money between B and C, which is given by 2:3
Given that A has the amount Rs.800
We have to find out how much C has.
Let the money that A has be = $4x$
Let the money that B has be = $5x$
As already given that A has Rs.800, hence equating $4x$ to Rs.800,
 $\Rightarrow 4x=800$
 $\Rightarrow x={\displaystyle \frac{800}{4}}$
 $\Rightarrow x=200$
B has is $5x$ , substituting the value of $x$ to get the amount of money B has.
The amount of money that B has is given by:
 $\Rightarrow 5x=5\left(200\right)$
 $\Rightarrow 1000$
 $\therefore$ The amount of money B has is Rs.1000.
Now we know that the ratio of money between B and C is 2:3
Let the money that B has be = $2y$
Let the money that C has be = $3y$
We found that B has Rs.1000, hence equating $$2y$$ to Rs.1000 ,
 $\Rightarrow 2y=1000$
 $\Rightarrow y={\displaystyle \frac{1000}{2}}$
 $\Rightarrow y=500$
C has $3y$ , substituting the value of $y$ to get the amount that C has.
The amount of money that C has is given by:
 $\Rightarrow 3y=3\left(500\right)$
 $\Rightarrow 1500$
 $\therefore$ The amount of money C has is Rs.1500.

Final Answer: The amount C has is Rs.1500.

Note:
While solving this problem please note that we did not directly calculate the money of C, first we assigned one variable $x$ to the ratio of money A and B has, then after finding the money that B has, we assigned another variable $y$ to the ratio of money of B and C, and then found the unknown amount of C has