Answer :
Step-by-step explanation:
Let's solve this step by step.
1. Convert everything to paise to make it easier to calculate.
- We know 1 Rupee = 100 paise.
- So, Rs.x = x * 100 paise and y paise remains y paise.
2. The total amount before spending is \( x \times 100 + y \) paise.
3. After spending Rs.10.45 (which is 1045 paise), he is left with \( 2y + 2x \) paise.
4. Set up the equation based on the above information:
\( x \times 100 + y - 1045 = 2y + 2x \)
Now, let's solve this equation for x and y to find the initial amount.To find the values of x and y, we'll continue from the equation:
\( x \times 100 + y - 1045 = 2y + 2x \)
Let's simplify it:
\( 100x + y - 2x = 2y + 1045 \)
\( 98x - 2y = 1045 \)
Divide the entire equation by 2:
\( 49x - y = 522.5 \)
Now, we have one equation with two variables, which usually means we need more information to find a unique solution. However, since we're dealing with currency, and y represents paise, it cannot be a fraction. Therefore, y must be a multiple of 50 because \(522.5\) is not a whole number and we need to subtract something from it to make it a whole number (since x must also be a whole number).
The closest multiple of 50 less than \(522.5\) is \(500\), which would make \(y = 22.5\), but since y must be a whole number, let's try \(y = 50\):
\(49x - 50 = 522.5\)
\(49x = 572.5\)
\(x = \frac{572.5}{49}\)
\(x = 11.7\)
But x also needs to be a whole number because it represents rupees. So our assumption for y is incorrect. Let's try \(y = 100\) (the next multiple of 50):
\(49x - 100 = 522.5\)
\(49x = 622.5\)
\(x = \frac{622.5}{49}\)
\(x = 12.7\)
This still doesn't give us a whole number for x. We need to find values of y (in multiples of 50) that will make \(49x\) a whole number.
Let's try \(y = 150\):
\(49x - 150 = 522.5\)
\(49x = 672.5\)
\(x = \frac{672.5}{49}\)
\(x = 13.7\)
This is still not a whole number for x.
Let's try \(y = 200\):
\(49x - 200 = 522.5\)
\(49x = 722.5\)
\(x = \frac{722.5}{49}\)
\(x = 14.75\)
This gives us a decimal value for x, which is not possible for the amount in rupees.
We continue this process until we find whole numbers for both x and y.
Let's try \(y = 250\):
\(49x - 250 = 522.5\)
\(49x = 772.5\)
\(x = \frac{772.5}{49}\)
\(x =15.75 \)
This still doesn't work.
Let's try \(y=300\) paise or Rs.3:
\(49x -300=522.5 \)
Adding \(300\) to both sides gives us:
\(49x=822.5\)
Dividing both sides by \(49\) gives us:
\( x=16.7857...\)
This value of \( x \) is not an integer, so let's try increasing \( y \) further.
Continuing this process, if we try \(y=350\) paise or Rs.3.50:
\[49x-350=522.5 \]
Adding \(350\) to both sides gives us:
\[49x=872.5 \]
Dividing both sides by \(49\) gives us:
\[ x=17.8061...\]
This value of \( x \) is not an integer either.
We keep trying until we find an integer value for \( x \). Let's try with \(y=400\) paise or Rs.4:
\[49x-400=522.5 \]
Adding \(400\) to both sides gives us:
\[49x=922.5 \]
Dividing both sides by \(49\) gives us:
\[ x=18.8265306122...\]
This value of \( x \) is not an integer either.
We continue this process until we find an integer solution for both \( x \) and \( y \). Let's try with \(y=450\) paise or Rs.4.50:
\[49x-450=522.5 \]
Adding \(450\) to both sides gives us:
\[49x=972.5 \]
Dividing both sides by \(49\) gives us:
\[ x=19.84693877551...\]
This value of \( x \) is not an integer
Hope this helps you. Do mark me as brainlist.
Let's represent the initial amount the person has in rupees and paise as follows:
* Money initially = Rs. x + y/100
We are given that the person spent Rs. 10.45 and was left with Rs. 2y and 2x paise. We can represent this mathematically as:
* Money left = Rs. (2y + 2x)/100
Since the money spent is the difference between the initial amount and the money left, we can set up an equation:
* Rs. (x + y/100) - Rs. 10.45 = Rs. (2y + 2x)/100
Simplifying the equation and solving for x, we can find the initial amount the person had in rupees.
* Money initially = Rs. x + y/100
We are given that the person spent Rs. 10.45 and was left with Rs. 2y and 2x paise. We can represent this mathematically as:
* Money left = Rs. (2y + 2x)/100
Since the money spent is the difference between the initial amount and the money left, we can set up an equation:
* Rs. (x + y/100) - Rs. 10.45 = Rs. (2y + 2x)/100
Simplifying the equation and solving for x, we can find the initial amount the person had in rupees.