Question

If Rs. 2800 is $ \dfrac{2}{7} $ percent of the value of a house, the worth of the house in (Rs.) is?
(a) $ 8,00,000 $
(b) $ 9,80,000 $
(c) $ 10,00,000 $
(d) $ 12,00,000 $

Answer 1

Hint: Let us assume that the value of house is x and it is given that $ \dfrac{2}{7} $ percent of the value of a house is Rs. 2800 so we can write this statement in terms of x as $ \dfrac{2}{7}\left( \dfrac{1}{100} \right)x=2800 $ . To get the value of x solve this equation. The value of x will give us the worth of the house.

Complete step-by-step answer:
Let us assume the worth of the house is Rs x.
It is given that $ \dfrac{2}{7} $ percent of the value of a house is Rs. 2800 so writing this statement mathematically we get,
 $ \dfrac{2}{7}\left( \dfrac{1}{100} \right)x=2800 $ ………. Eq. (1)
Multiplying 700 on both the sides we get,
 $ 2x=2800\left( 700 \right) $
Dividing 2 on both the sides to get the value of x we get,
 $ x=\dfrac{2800\left( 700 \right)}{2} $
In the above equation, multiplication of 2800 by 700 will give 1960000.
 $ x=\dfrac{1960000}{2} $
On dividing the right hand side of the above equation by 2 we get,
 $ x=980000 $
From the above calculations, we have calculated the worth of a house as Rs. 9, 80, 000.
Hence, the correct option is (b).

Note: Instead of solving the above method completely stop after eq. (1) in the above solution and then in place of x in eq. (1) substitute all the options given in the question and then see which option is satisfying the eq. (1).
 $ \dfrac{2}{7}\left( \dfrac{1}{100} \right)x=2800 $
This is the eq. (1) so let us substitute the option (a) in place of x which is 800000 in the above equation we get,
 $ \begin{align}
  & \dfrac{2}{7}\left( \dfrac{1}{100} \right)\left( 800000 \right)=2800 \\
 & \Rightarrow \dfrac{2}{7}\left( 8000 \right)=2800 \\
 & \Rightarrow \dfrac{16000}{7}=2800 \\
 & \Rightarrow 2285.7=2800 \\
\end{align} $
From the above you can see that L.H.S is not equal to R.H.S so option (a) is not satisfying the equation and hence, option (a) is incorrect.
Similarly, check other options and see which option is satisfying eq. (1). The one which satisfies eq. (1) is the correct option.