Manohar has total of rs 250 as currency notes in the denomination of rs 20 ,rs10 and rs 5. The ratio of the numbers of rs 20 notes and rs10 notes is 3:4. If he has a total of 24 notes,how many notes of each denomination he has?
A sum of Rs 500 is in form of domination of Rs 5 and Rs 10 if the total number of notes is 90 find the number of notes of each type
Let's assume the number of Rs 20 notes in Manohar's possession is 3x, and the number of Rs 10 notes is 4x.
Now, we can calculate the total value of the Rs 20 notes and the Rs 10 notes:
Value of Rs 20 notes = 20 * (3x) = 60x
Value of Rs 10 notes = 10 * (4x) = 40x
We are given that the total value of all the notes is Rs 250, so we can write the equation:
60x + 40x + (amount of Rs 5 notes) = 250
Simplifying the equation, we get:
100x + (amount of Rs 5 notes) = 250
We also know that the total number of notes is 24, so we can write another equation:
3x + 4x + (amount of Rs 5 notes) = 24
Simplifying this equation, we get:
7x + (amount of Rs 5 notes) = 24
Now, we have a system of equations:
100x + (amount of Rs 5 notes) = 250
7x + (amount of Rs 5 notes) = 24
Subtracting the second equation from the first equation, we eliminate the "amount of Rs 5 notes" variable:
100x + (amount of Rs 5 notes) - 7x - (amount of Rs 5 notes) = 250 - 24
93x = 226
x ≈ 2.43
Since x represents the number of sets of 3 Rs 20 notes and 4 Rs 10 notes, which must be a whole number, we can round down to x = 2.
Therefore, Manohar has:
3x = 3 * 2 = 6 Rs 20 notes,
4x = 4 * 2 = 8 Rs 10 notes.
To find the number of Rs 5 notes, we substitute x = 2 into one of the equations:
7x + (amount of Rs 5 notes) = 24
7 * 2 + (amount of Rs 5 notes) = 24
14 + (amount of Rs 5 notes) = 24
(amount of Rs 5 notes) = 24 - 14 = 10
Therefore, Manohar has:
6 Rs 20 notes,
8 Rs 10 notes, and
10 Rs 5 notes.
To solve this problem, let's break it down into smaller steps.
Step 1: Define the variables.
Let x be the number of Rs 20 notes.
Let y be the number of Rs 10 notes.
Let z be the number of Rs 5 notes.
Step 2: Write the given information as equations.
We know that the ratio of the number of Rs 20 notes to Rs 10 notes is 3:4.
This can be written as: x/y = 3/4
We also know that the total number of notes is 24.
So, x + y + z = 24
Step 3: Solve the equations.
Since we have two equations, we can use substitution or elimination method to solve for the variables.
Let's use the substitution method:
From the first equation, we can express x in terms of y:
x = (3/4)y
Substituting this in the second equation:
(3/4)y + y + z = 24
(7/4)y + z = 24
Step 4: Simplify the equation.
To get rid of the fraction, we can multiply both sides of the equation by 4:
4(7/4)y + 4z = 24 * 4
7y + 4z = 96
Step 5: Explore the possibilities for y and z.
We know that y and z must be positive integers because they represent the number of notes.
By trial and error, we can find the combinations of y and z that satisfy the equation:
- If y = 8 and z = 8, then 7(8) + 4(8) = 96.
- If y = 12 and z = 5, then 7(12) + 4(5) = 96.
Step 6: Find the value of x.
We can substitute the values of y and z into the first equation to find x:
x = (3/4)y
- If y = 8, then x = (3/4)(8) = 6.
- If y = 12, then x = (3/4)(12) = 9.
Therefore, there are two possible combinations of notes:
1) Rs 20 notes: 6, Rs 10 notes: 8, Rs 5 notes: 8
2) Rs 20 notes: 9, Rs 10 notes: 12, Rs 5 notes: 5