Question

A bag contains \[Rs.{\text{ }}600\]in the form of \[1{\text{ }}rupee,{\text{ }}50paise\] and \[25{\text{ }}paise\] coins in the ratio \[3:4:12.\]The number of \[25{\text{ }}paise\] coins is:

A. $600$
B. $800$
C. $1200$
D. $900$

Answer 1

Hint- In order to solve this question first we will convert paise into rupees by dividing paise with \[100\]more we will assume the number of coins as a variable of \[1{\text{ }}rupee,{\text{ }}50paise\] and \[25{\text{ }}paise\]and we will make an equation with a single variable according to the given ratio, and by solving it we will get the required answer.

Complete step-by-step answer:
The statement is a bag includes \[Rs.{\text{ }}600\] in the form of \[1{\text{ }}rupee,{\text{ }}50paise\]and \[25{\text{ }}paise\]coins in the \[3:4:12.\] ratio.
Firstly we need to convert paise into Rs
As we know that
\[100{\text{ }}paise{\text{ }} = {\text{ }}1{\text{ }}rup\]
Let no of one rupee coins be \[3X,{\text{ }}50{\text{ }}paise\] coins be \[4X{\text{ }}and{\text{ }}25{\text{ }}paise\] coins be \[12X\]
Amount of \[1{\text{ }}rupee\] coins would be \[Rs{\text{ }}3X\]
Amount of \[50{\text{ }}paise\] coins would be \[ = {\text{ }}\left( {{\text{ }}4X{\text{ }} \times {\text{ }}0.5} \right){\text{ }} = {\text{ }}2X\]
Amount of \[25{\text{ }}paise\] coins would be \[\left( {12X{\text{ }} \times {\text{ }}0.25} \right){\text{ }} = {\text{ }}3X\]
Now given that total amount in bag is \[600{\text{ }}Rs\]
So by adding all the amount we get
$3X + 2X + 3X = 600$
By solving above equation we get
$
  X = 600/8 \\
  X = 75 \\
 $

Therefore number of \[25{\text{ }}paise\] coins \[ = {\text{ }}12{\text{ }} \times {\text{ }}75{\text{ }} = {\text{ }}900\]

Hence the correct answer is option D.

Note- A ratio is a way to measure two numbers, using division as we measure miles and hours in miles per hour. On the other hand, a proportion is an equation which states that two ratios are equal. When one number is unknown in a proportion the number can be identified by solving the proportion.