Question

A purse contains Rupees 10,800 in terms of 50 paise, 2 rupees and 5 rupees coins in the ratio 2:3: 4. Find the number of each type of coins.​

Answer 1

Step-by-step explanation:

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Answer 2

$\large\underline\blue{\bold{Given \:  Question :-  }}$

• A purse contains Rupees 10,800 in terms of 50 paise, 2 rupees and 5 rupees coins in the ratio 2: 3: 4. Find the number of each type of coins.

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$\huge{AηsωeR} ✍$

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$\large\underline\blue{\bold{Given :-  }}$

• A purse contains Rupees 10,800 in terms of 50 paise, 2 rupees and 5 rupees coins in the ratio 2 : 3 : 4.

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$\large\underline\blue{\bold{To \: Find :-  }}$

• The number of each type of coins in purse.

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✏️ Let understand the concept :-

For solving such problems, the ratio of coins are given. We first suppose the number of coins in terms of x as x, 3x 4x individually. Then we represent the all the prices in terms of x and on adding all the prices of coins in terms of x and equate with ₹ 10, 800, we get the value of 'x'. Then we easily evaluate the number of coins in purse.

★ Note :-

• An important step involving in this problem is the conversion of given currency in to a standard form. Since the total amount is in rupees, so all the currencies are converted into rupees.

Let's do the problem!!

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$\large\underline\purple{\bold{Solution :- }}$

$\begin{gathered}\begin{gathered}\bf Let= \begin{cases} &\sf{number \: of \: 50 \: paisa \: coin \: be \: 2x} \\ &\sf{number \: of \: ₹ \: 2 \: coins \: be \: 3x}\\ &\sf{number \: of \:₹ \: 5 \: coins \: be \: 4x } \end{cases}\end{gathered}\end{gathered}$

★ Now, total amount of 50 paisa coin in purse = 50 × 2x = 100x paisa = ₹ x

★ Total amount of ₹ 2 in purse = 2 × 3x = 6x

★ Total amount of ₹ 5 in purse = 5 × 4x = 20x

★ Now, Total amount in purse = ₹ 10, 800

$\bf\implies \: \: x + 6x + 20x = 10800$

$\sf \:  ⟼27x = 10800$

$\sf \:  ⟼x = {\cancel\dfrac{10800}{27}400}$

$\begin{gathered}\begin{gathered}\bf So= \begin{cases} &\sf{number \: of \: 50 \: paisa \: coin \: be \: 2 \times 400 = 800} \\ &\sf{number \: of \: ₹ \: 2 \: coins \: be \: 3 \times 400 = 1200}\\ &\sf{number \: of \:₹ \: 5 \: coins \: be \: 4 \times 400 = 1600} \end{cases}\end{gathered}\end{gathered}$