Question

A bag contains \[25\] paise, \[10\] paise and \[5\] paise coins in the ratio \[1:2:3.\] If their total value is Rs. \[30,\] the number of \[5\] paise coins is
A. \[50\]
B. \[100\]
C. \[150\]
D. \[200\]

Answer 1

Hint: To solve this question, we will start with assuming the given ratios, i.e., \[25\] paise be \[x,\] \[10\] paise be \[2x,\] \[5\] paise into \[3x.\] Then, on taking the total number of coins to the total value, i.e., Rs. 30, we will make a linear equation with it. then after getting the value of x, and then after putting the value of x, we will get our required answer.

Complete step-by-step answer:
We have been given a bag that contains \[25\] paise, \[10\] paise and \[5\] paise coins in the ratio \[1:2:3.\] It is given that the total value is \[Rs.{\text{ }}30,\] we need to find the number of \[5\] paise coins in the given bag.
Let the number of \[25\] paise, \[10\] paise and \[5\] paise coins be \[x,2x\] and \[3x\] respectively.
Then, the total value of all the coins given \[ = {\text{ }}25x{\text{ }} + {\text{ }}10\left( {2x} \right){\text{ }} + {\text{ }}\left( 5 \right)3x{\text{ }} = {\text{ }}60x\] paisa
Now, it is given that the total value of coins in the bag is Rs. \[30.\]
We know that, Re. \[1{\text{ }} = {\text{ }}100\] paisa
So, Rs. \[30{\text{ }} = {\text{ }}30{\text{ }} \times {\text{ }}100\;\] paisa \[ = {\text{ }}300\] paisa
According to the question, total number of coins present in that bag is equals to Rs.\[\;30.\]
\[ \Rightarrow 60x{\text{ }} = {\text{ }}30{\text{ }} \times {\text{ }}100\;\] paise
\[ \Rightarrow x{\text{ }} = {\text{ }}50\]
Earlier, we have assumed that let \[5\;\] paise coins be \[3x.\] So, on putting the value of x, we get
Number of \[5\;\] paise coins \[ = {\text{ }}3x{\text{ }} = {\text{ }}150.\]
Thus, option (C) \[150\], is correct.
So, the correct answer is “Option C”.

Note: Students should take care that in these types of questions, the total number of coins is always equal to the total value of the amount given. That’s why we have taken the total number of twenty-five paisa, ten paise and five paisa coins equals to total value, i.e., thirty rupees, to get the required answer.