Question

Find the value of $\dfrac{\left( P+Q \right)}{R}\times S$
(i) 100 lakhs = ______ [Q] millions
(ii) _______ [R]crores = 100 millions
(iii) 100 thousands = _______[P] lakhs
(iv) 10 crores = ___________[S] millions
A. 10
B. 100
C. 110
D. 1

Answer 1

Hint: We need to find the value of the expression $\dfrac{\left( P+Q \right)}{R}\times S$ . We start to solve the given question by performing the unit conversions from lakhs to millions, crores to millions, thousands to lakhs, and crores to millions to find out the values of $P,Q,R,S\;$. Then, we substitute the value of $P,Q,R,S\;$ in the expression to get the desired result.

Complete step by step solution:
We are asked to find the value of the expression $\dfrac{\left( P+Q \right)}{R}\times S$ . We will be solving the given question by performing the unit conversions from lakhs to millions, crores to millions, thousands to lakhs, and crores to millions to find out the values of $P,Q,R,S\;$ and substituting them in the given expression.

From mathematics, we know that
$\Rightarrow 1\text{ million = 10 lakh}$
The value of $Q$ can be found as follows,
$\Rightarrow 1\text{ million = 10 lakh}$
$\Rightarrow Q\text{ million = 100 lakh}$
Cross multiplying to find the value of $Q$ , we get,
$\Rightarrow Q\text{ million}=\dfrac{100\text{ lakh }\times \text{1 million}}{10\text{ lakh}}$
Simplifying the above equation, we get,
$\therefore Q=10\text{ }$
From the above,
$\Rightarrow \left[ R \right]crore\text{ }=\text{ }100\text{ }million$
Cross multiplying to find the value of $R$ , we get,
$\Rightarrow R=\dfrac{100\text{ million}}{\text{crore}}$
We know that a million is numerically equal to 1000000 and a crore is numerically equal to 10000000.
Substituting the same, we get,
$\Rightarrow R=\dfrac{100\times 1000000}{10000000}$
Simplifying the above equation, we get,
$\therefore R=10$
From the question, we know that
$\Rightarrow 100\text{ }thousand\text{ }=\text{ P }lakh$
Cross multiplying to find the value of $P$ , we get,
$\Rightarrow P=\dfrac{100\text{ thousand}}{lakh}$
We know that a thousand is numerically equal to 1000 and a lakh is numerically equal to 100000.
Substituting the same, we get,
$\Rightarrow P=\dfrac{100\times 1000}{100000}$
Simplifying the above equation, we get,
$\therefore P=1$
The value of $S$ can be found out as follows,
$\Rightarrow 10\text{ }crore\text{ }=\left[ S \right]\text{ }million$
Cross multiplying to find the value of $S$ , we get,
$\Rightarrow S=\dfrac{10\text{ crore}}{million}$
We know that a crore is numerically equal to 10000000 and a million is numerically equal to 1000000.
Substituting the same, we get,
$\Rightarrow S=\dfrac{10\times 10000000}{1000000}$
Simplifying the above equation, we get,
$\therefore S=100$
Writing down the values of $P,Q,R,S\;$, we get,
P = 1;
Q = 10;
R = 10;
S = 100
Substituting the values in the expression$\dfrac{\left( P+Q \right)}{R}\times S\;$ , we get,
$\Rightarrow \dfrac{\left( P+Q \right)}{R}\times S=\dfrac{\left( 1+10 \right)}{10}\times 100$
Simplifying the above expression, we get,
$\Rightarrow \dfrac{\left( P+Q \right)}{R}\times S=\dfrac{\left( 11 \right)}{10}\times 100$
$\Rightarrow \dfrac{\left( P+Q \right)}{R}\times S=1.1\times 100$
$\therefore \dfrac{\left( P+Q \right)}{R}\times S=110$

So, the correct answer is “Option C”.

Note: We must avoid making mistakes in terms of calculations and conversion of units to get an accurate result. We have found the value of the variable Q using the unitary method. In the unitary method, we always write the things to be calculated on the right-hand side and things known on the left-hand side.