Sohan's father went to Nepal Bank Limited to get new notes of Rs 8500 for Dashain Tika. So he requested for notes of Rs 100 and Rs 5 and the bank gavt him 185 notes in total. Find how many notes are there of each rupees.

Let's denote the number of Rs 100 notes as \( x \) and the number of Rs 5 notes as \( y \). We are given the following information: 1. The total amount of money is Rs 8500. 2. The total number of notes is 185. We can set up the following equations based on the given information: 1. The total amount of money equation: \( 100x + 5y = 8500 \) 2. The total number of notes equation: \( x + y = 185 \) We can solve this system of equations to find the values of \( x \) and \( y \), which represent the number of Rs 100 and Rs 5 notes, respectively. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}100x+5y=8500\\x+y=185\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}100x+5y=8500\\x=185-y\end{array}\right.\) - step2: Substitute the value of \(x:\) \(100\left(185-y\right)+5y=8500\) - step3: Simplify: \(18500-95y=8500\) - step4: Move the constant to the right side: \(-95y=8500-18500\) - step5: Subtract the numbers: \(-95y=-10000\) - step6: Change the signs: \(95y=10000\) - step7: Divide both sides: \(\frac{95y}{95}=\frac{10000}{95}\) - step8: Divide the numbers: \(y=\frac{2000}{19}\) - step9: Substitute the value of \(y:\) \(x=185-\frac{2000}{19}\) - step10: Simplify: \(x=\frac{1515}{19}\) - step11: Calculate: \(\left\{ \begin{array}{l}x=\frac{1515}{19}\\y=\frac{2000}{19}\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}x=\frac{1515}{19}\\y=\frac{2000}{19}\end{array}\right.\) - step13: Rewrite: \(\left(x,y\right) = \left(\frac{1515}{19},\frac{2000}{19}\right)\) The solution to the system of equations is: - The number of Rs 100 notes (\( x \)) is \( \frac{1515}{19} \) or approximately 79.47. - The number of Rs 5 notes (\( y \)) is \( \frac{2000}{19} \) or approximately 105.26. Since the number of notes must be whole numbers, we can round these values to the nearest whole numbers: - The number of Rs 100 notes is 80. - The number of Rs 5 notes is 105. Therefore, Sohan's father received 80 Rs 100 notes and 105 Rs 5 notes in total.