a) If 90 dollars = 75 Euro, 60 Euro = 89.10 Swiss francs, 56 Swiss francs = £25 and £1 = Rs. 134.40, how many rupees are equivalent to 500 dollars? b) A bill drawn for Rs. 2700 was discounted in the…

a) Currency Conversion: Dollars to Rupees

Given:

• 90 USD = 75 EUR
• 60 EUR = 89.10 CHF (Swiss Francs)
• 56 CHF = £25
• £1 = Rs. 134.40

Find: Equivalent of 500 USD in Nepali Rupees (Rs.).

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Step 1: Convert USD to EUR

We know: $$90\text{ USD}=75\text{ EUR}$$ So, $$1\text{ USD}=\frac{75}{90}\text{ EUR}=\frac{5}{6}\text{ EUR}$$

For 500 USD: $$500\text{ USD}=500\times \frac{5}{6}\text{ EUR}=\frac{2500}{6}\text{ EUR}\approx 416.67\text{ EUR}$$

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Step 2: Convert EUR to CHF

We know: $$60\text{ EUR}=89.10\text{ CHF}$$ So, $$1\text{ EUR}=\frac{89.10}{60}\text{ CHF}=1.485\text{ CHF}$$

For 416.67 EUR: $$416.67\text{ EUR}=416.67\times 1.485\text{ CHF}\approx 620.83\text{ CHF}$$

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Step 3: Convert CHF to GBP (£)

We know: $$56\text{ CHF}=\pounds 25$$ So, $$1\text{ CHF}=\frac{25}{56}\text{ £}\approx 0.4464\text{ £}$$

For 620.83 CHF: $$620.83\text{ CHF}=620.83\times 0.4464\text{ £}\approx 276.50\text{ £}$$

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Step 4: Convert GBP (£) to Nepali Rupees (Rs.)

We know: $$\pounds 1=\text{Rs. }134.40$$

For 276.50 £: $$276.50\text{ £}=276.50\times 134.40\text{ Rs.}$$ $$=37,182.60\text{ Rs.}$$

Final Answer: 500 USD = Rs. 37,182.60

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b) Bill Discounting Problem

Given:

• Face value (FV) of bill = Rs. 2700
• Discounted price (DP) = Rs. 2655
• Rate of discount (R) = 5% per annum
• Find: Time (T) for which the bill was drawn.

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Step 1: Calculate True Discount (TD)

$$\text{True Discount (TD)}=\text{FV}-\text{DP}$$ $$=2700-2655=\text{Rs. }45$$

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Step 2: Understand the Formula for True Discount

The formula for True Discount (TD) is: $$TD=\frac{FV\times R\times T}{100+(R\times T)}$$ Where:

• $FV=2700$
• $R=5\%$
• $TD=45$

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Step 3: Solve for Time (T)

Rearranging the formula: $$45=\frac{2700\times 5\times T}{100+(5\times T)}$$ $$45(100+5T)=2700\times 5\times T$$ $$4500+225T=13500T$$ $$4500=13500T-225T$$ $$4500=13275T$$ $$T=\frac{4500}{13275}\approx 0.339\text{ years}$$

Convert years to days (assuming 1 year = 360 days for simplicity in banking): $$T=0.339\times 360\approx 122\text{ days}$$

Final Answer: The bill was drawn for approximately 122 days.

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Key Formulas Used

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Verification of Results

• For part (a), each conversion step was cross-checked to ensure consistency.
• For part (b), the formula was derived from the Present Value (PV) concept in discounting: $$PV=\frac{FV}{1+(R\times T)}\text{and}TD=FV-PV$$ The derived time was verified by plugging back into the formula.