A box of paisa

A box contains 261 coins valued at 20 paisa, 25 paisa, and 50 paisa. Their total values in rupees are in the ratio 7:8:10. Find the number of 25 paisa coins. (Note: 1 Rupee = 100 Paise.)

Final Answer:

b =  96

Step-by-step explanation:

$$\begin{gathered} a+b+c=261 \\ 0.2a+0.25b+0.50c=s \\ 0.20a:0.25b:0.50c=7:8:10 \\ 20a:25b:50c=7:8:10 \\ 0.20a=\frac{7}{7+8+10}\cdot s=\frac{7}{25}s \\ 0.25b=\frac{8}{7+8+10}\cdot s=\frac{8}{25}s \\ 0.50a=\frac{10}{7+8+10}\cdot s=\frac{10}{25}s \\ a+b+c=261 \\ \frac{7/0.20}{25}s+\frac{8/0.25}{25}s+\frac{10/0.50}{25}s=261 \\ 7/0.2\cdot s+8/0.25\cdot s+10/0.50\cdot s=261\cdot 25=6525 \\ 87s=6525 \\ s=6525/87=75 \\ a=\frac{7}{25\cdot 0.20}\cdot s=\frac{7}{25\cdot 0.20}\cdot 75=105 \\ b=\frac{8}{25\cdot 0.25}\cdot s=\frac{8}{25\cdot 0.25}\cdot 75=96 \\ c=\frac{10}{25\cdot 0.50}\cdot s=\frac{10}{25\cdot 0.50}\cdot 75=60 \\ \text{ Verifying Solution: } \\ {s}_2=a+b+c=105+96+60=261 \end{gathered}$$

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