Question

If $$\dfrac{4}{5}$$ of an estate worth Rs.16,800, then value of $$\dfrac{3}{7}$$ of these estate is
A. Rs. 9,000
B. Rs. 21,000
C. Rs. 72,000
D. Rs. 90,000

Answer 1

Hint: In this question it is given that if $$\dfrac{4}{5}$$ of an estate worth Rs.16,800, then we have to find the value of $$\dfrac{3}{7}$$ of these estate. So to find the solution we need to first consider the value of the estimate and after that by using the given information we are able to find the solution.
Also we need to know that if we are given ‘$$\dfrac{m}{n}$$ part of x’ then we can write this as $$\dfrac{m}{n} \times x$$.

Complete step-by-step answer:
Let us consider that the value of estate is x.
Here it is given that $$\dfrac{4}{5}$$ of an estate worth Rs.16,800, in other words we can say that $$\dfrac{4}{5}$$ of x worth Rs.16,800,
So $$\dfrac{4}{5}$$ of x is $$\dfrac{4}{5} \times x$$, which is equals to 16,800
So in equational form we can write,
$$\dfrac{4}{5} \times x=16800$$
$$\Rightarrow \dfrac{4x}{5} =16800$$
$$\Rightarrow 4x=16800\times 5$$
$$\Rightarrow x=\dfrac{16800\times 5}{4}$$ [dividing both side by 4]
$$\Rightarrow x=\dfrac{4\times 4200\times 5}{4}$$
$$\Rightarrow x=4200\times 5$$
$$\Rightarrow x=21000$$
Therefore the value of the estate is Rs. 21,000.
Now we have to find $$\dfrac{3}{7}$$ of the estate, i.e $$\dfrac{3}{7}$$ of Rs. 21,000.
$$\therefore$$ $$\dfrac{3}{7}$$ of Rs. 21,000
    =$$\text{Rs.} \ \left( \dfrac{3}{7} \times 21000\right) $$
    =$$\text{Rs.} \ \left( \dfrac{3}{7} \times 7\times 3000\right) $$
    =$$\text{Rs.} \ \left( 3\times 3000\right) $$
    =Rs. 9000
Hence the correct option is option A.

Note: While solving this type of question you need to know that whenever you have given that $$\dfrac{m}{n}$$ of any quantity then it implies that you have to divide the given quantity into n number of parts and from where you have to take m number of parts. For example, $$\dfrac{4}{5}$$ of x means we have to make 5 parts of x, from which 4 parts we have to take.