Mona has 25 Paisa coins,50 Paisa coins.the number of 25 Paisa coins is thrice the number of 50 Paisa coin.if the total value of money is R.75, find the number of 25 paisa coins and 50 Paisa coins she has?
Answers
Step-by-step explanation:
Number of 50 paise coins and number 25 paise coins in purse are 60 and 180 respectively.
Explanation :-
Let the number of 50 paise coins be x
Number of 25 paise coins = thrice the number of of 50 paise coins = 3 * x = 3x
Value of all 50 paise i.e Rs. 1/2 coins in purse = 1/2 * Number of 50 paise coins = 1/2 * 3x = Rs. x/2
Value of all 25 paise i.e Rs. 1/4 coins in purse = 1/4 * Number of 25 paise coin is = 1/4 * 3x = Rs. 3x/4
Total value of money in the purse = Rs. 75
Value of all 50 paise coins in purse + Value of all 25 paise coins in purse = Rs. 75
\begin{gathered}\sf \implies \dfrac{x}{2} + \dfrac{3x}{4} = 75 \\ \\ \\ \tt \underline{taking \ LCM} \\ \\ \\ \sf \implies \dfrac{x(2) + 3x}{4} = 75 \\ \\ \\ \sf \implies \dfrac{2x + 3x}{4} = 75 \\ \\ \\ \sf \implies \dfrac{5x}{4} = 75 \\ \\ \\ \sf \implies 5x = 75 \times 4 \\ \\ \\ \sf \implies 5x = 300 \\ \\ \\ \sf \implies x = \dfrac{300}{5} \\ \\ \\ \sf \implies x = 60\end{gathered}
⟹
2
x
+
4
3x
=75
taking LCM
⟹
4
x(2)+3x
=75
⟹
4
2x+3x
=75
⟹
4
5x
=75
⟹5x=75×4
⟹5x=300
⟹x=
5
300
⟹x=60
i.e Number 50 paise coins = 60
Number of 25 paise coin = 3x = 3(60) = 180
Therefore number of 50 paise coins and number 25 paise coins in purse are 60 and 180 respectively.