Question

An international bank issues its Traveler credit cards worldwide. When a customer makes a purchase using a Traveler card in currency different from the customer's home currency, the bank converts the purchase price at the daily foreign exchange rate and then charges a 4% fee on the converted cost.
Sara lives in the United States, but is on vacation in India. She used her Traveler card for a purchase that cost 602 rupees (Indian currency). The bank posted a charge \[\ $ 9.88\] to her account that included the 4% fee.
What foreign exchange rate, in Indian rupee per one U.S dollar, did the bank use for Sara's charge? Round your answer to the nearest whole number.

Answer 1

Hint: Money is a exchanging source to every goods and product, the currency is different in different places, like so the value of the currency is different from different places, for example the currency of America is Dollars whereas India is Rupee but the values of both currencies are not same, the value of one United States Dollar is approximately 60-70 Rupees. So in this solution, we have to find the Indian rupees that had been paid to the vendor by Sara to purchase an item.

Complete step-by-step answer:
The exchange charge is\[\;x = 4\% = 0.04\].
The amount that Sara purchased an item is \[A = {\rm{Rs}}{\rm{. }}602\].
The amount that the bank posted a charge at Sara is $z = \$ 9.88$.
We know the equation to find the amount bank charged Sara for the purchase is,
\[X = \dfrac{z}{{1 + x}}\]
On substituting the values in the above equation, we get the value,
\[\begin{array}{c}
X = \dfrac{{\$ 9.88}}{{1 + 0.04}}\\
 = \dfrac{{9.88}}{{1.04}}\\
 = \$ 9.5
\end{array}\]
Since, the equation to find the exchange rate, in Indian rupee to U.S dollar is given as,
$y = \dfrac{A}{X}$
On substituting the values in the above equation, we get the value,
\[\begin{array}{c}
y = \dfrac{A}{X}\\
 = \dfrac{{602\,}}{{9.55}}\\
 = 63.37\\
 \approx \$ 63\,
\end{array}\]
Therefore, the bank charged for the purchase is \[\$ 9.5\]and the exchange rate in Indian rupees from dollar is \[\$ 63\,\].

Note: While solving the problem, understanding the difference between the exchange rate and the charges applied on it, the charging fees here is 4% it means, we have to take out the charging fees while we are calculating the foreign exchange difference. And remember that the digits of money are less for America because it has high value, so we have to place it in the denominator and the Indian rupee should be in the numerator.