Collecting money

Rs 180 contained in a box of one rupee, 50 Paise and 25 Paise coins in the ratio 2:3:4. What is the number of 50 Paise coins?
(One rupee = 100 paisa)

Correct answer:

b =  120

Step-by-step explanation:

$$\begin{gathered} 180=a+0.5b+0.25c \\ a:b:c=2:3:4=2x:3x:4x \\ a=2x \\ b=3x \\ c=4x \\ 180=2x+0.5\cdot 3x+0.25\cdot 4x \\ 180=2\cdot x+0.5\cdot 3\cdot x+0.25\cdot 4\cdot x \\ 4.5x=180 \\ x=\frac{180}{4.5}=40 \\ x=40 \\ a=2\cdot x=2\cdot 40=80 \\ b=3\cdot x=3\cdot 40=120 \\ c=4\cdot x=4\cdot 40=160 \end{gathered}$$

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