Question

Suppose A, B, C have Rs. a, Rs. b, Rs. c respectively. If $a:b = 4:5$ , $b:c = 2:3$ and a = 800, Find the value of c.

Answer 1

Hint: In this question, we will just consider the first ratio and just put the value of a there to get the value of b. Then we will just take the second ratio given and just put the value of b there to get the required value of c.

Complete step-by-step answer:
It is given that, $a:b = 4:5$
$ \Rightarrow \dfrac{a}{b} = \dfrac{4}{5}$
Now the given value of a is 800, substitute that in the above equation.
$ \Rightarrow \dfrac{{800}}{b} = \dfrac{4}{5}$
On cross multiplying we get,
$ \Rightarrow 800 \times 5 = 4 \times b$
$ \Rightarrow 4000 = 4 \times b$
On dividing both sides by 4 we get,
$ \Rightarrow \dfrac{{4000}}{4} = b$
\[ \Rightarrow 1000 = b\] or \[b = 1000\]
So, the value of b is 1000
Now, it is also given that $b:c = 2:3$
$ \Rightarrow \dfrac{b}{c} = \dfrac{2}{3}$
Now we know the value of b is 1000, substitute that in the above equation.
$ \Rightarrow \dfrac{{1000}}{c} = \dfrac{2}{3}$
On cross multiplying we get,
$ \Rightarrow 1000 \times 3 = 2 \times c$
$ \Rightarrow 3000 = 2 \times c$
On dividing both sides by 2 we get,
$ \Rightarrow \dfrac{{3000}}{2} = c$
\[ \Rightarrow 1500 = c\] or \[c = 1500\]
Hence, the value of c is 1500
$\therefore $ c = Rs. 1500 is our required answer or C has Rs. 1500.


Note- In such types of questions, just simply consider the ratios and find the variables one by one using simple arithmetic techniques including cross multiplication, division to create the equations and simplifying them to get the answer.