Question

Find the value of $ \left( {\dfrac{{P + Q}}{R}} \right) \times S $
A. $ 100{\text{ lakhs = \_\_\_\_\_ [Q] millions}} $
B. $ \_\_\_\_\_\_[R]{\text{ crores = 100 millions}} $
C. $ 100{\text{ thousands = \_\_\_\_\_\_ [P] lakhs}} $
D. $ 10{\text{ crores = \_\_\_\_\_ [S] millions}} $

Answer 1

Hint: It is a well-known fact that $ 1{\text{ million}} $ is equal to $ 10{\text{ lakhs}} $ . We are also aware that $ 1{\text{ crore}} $ is equal to $ 100{\text{ lakhs}} $ . Use a substitution method to substitute these facts in the proper place so that it reduces the complication of this question. Also, use addition, subtraction, multiplication and division operators in order to find the value of each of the blanks. Apply the values present in the blanks to the given expression and find the final solution.Solution:

Complete step-by-step answer:
It is a well-known fact that $ 1{\text{ million = 10 lakhs}} $ .
After multiplying the equation by 10, we get,
 $ 10{\text{ million = 100 lakhs}} $
Therefore, the value of $ Q $ is equal to 10.
We know that, $ 1{\text{ crore = 100 lakhs}} $ and $ 10{\text{ million = 100 lakhs}} $ .
So, after comparing both the equations we get, $ 1{\text{ crore = 10 millions}} $ .
After multiplying the equation by 10, we get, $ 10{\text{ crore = 100 millions}} $
Therefore, the value of $ R $ is equal to 10.
 $ 100{\text{ thousands = 100}} \times {\text{1000}} $ which is equal to $ {10^5} $ i.e. $ 1{\text{ lakh}} $ .
So, $ 100{\text{ thousands = 1 lakh}} $ .
Therefore, the value of $ P $ is 1.
We know that, $ 1{\text{ crore = 100 lakhs}} $ and $ 10{\text{ million = 100 lakhs}} $ .
So, after comparing both the equations we get, $ 1{\text{ crore = 10 millions}} $ .
On multiplying both sides of the equation by 10, we get, $ 10{\text{ crore = 100 millions}} $ .
Therefore, the value of $ S $ is equal to 100.
After solving the fill in the blanks, we have got the values of $ P,{\text{ }}Q,{\text{ }}R,{\text{ }}S $
Now, substitute the values of $ P = 1,\;Q = 10,\;R = 10,\;S = 100 $ in the expression $ \left( {\dfrac{{P + Q}}{R}} \right) \times S $ .
 $
\Rightarrow \left( {\dfrac{{P + Q}}{R}} \right) \times S = \left( {\dfrac{{1 + 10}}{{10}}} \right) \times 100\\
 = \dfrac{{11}}{{10}} \times 100\\
 = 110
$
Therefore, the value of $ \left( {\dfrac{{P + Q}}{R}} \right) \times S $ is equal to 110.

Note: Keep in mind that $ 1{\text{ million = 10 lakhs}} $ and $ 1{\text{ lakh }} \ne {\text{ 10 millions}} $ . Students might get confused and might use the wrong value instead of the right value i.e. $ 1{\text{ million = 10 lakhs}} $ . Also, students should keep in mind the basic conversions. Appropriate operations such as multiplication or division are to be done in order to find the solutions in this type of question.