A hundred rupee note was changed into 5 rupees notes and 20 rupees notes.if there are 11 notes in all. find the number of each type of notes?
Answers
Let there be x five re note and y twenty re note
x+y = 11.....(1)
x×5 + y×20 = 100
x + 4y = 20.....(2)
Subtract (1) from (2)
3y = 20 - 11 = 9
y = 3
x = 11 - 3 =8
Ans 8 five re note and 3 twenty re note
Answer :
›»› The number of each types of notes are 3 and 8.
Given :
- A hundred rupee note was changed into 5 rupees notes and 20 rupees notes.
- If there are 11 notes in all.
To Find :
- The number of each type of notes.
Solution :
Let,
The number of 5 rupee notes be "x" and the number of 20 rupee notes be "y"
Total number of notes = 11
→ x + y = 11 .....(1)
Multiply equation (1) by 5
→ 5(x + y = 11)
→ 5x + 5y = 55 .....(2)
A hundred rupee note was changed into 5 rupees notes and 20 rupees notes.
→ 20x + 5y = 100 .....(3)
Our equations are,
- x + y = 11 .....(1)
- 5x + 5y = 55 .....(2)
- 20x + 5y = 100 .....(3)
Subtract equation (3) from equation (2)
→ (5x + 5y = 55) - (20x + 5y = 100)
→ (5x + 5y) - (20x + 5y) = -55 - 100
→ (5x + 5y) - (20x + 5y) = -45
→ 5x + 5y - 20x - 5y = -45
→ 5x - 20x = -45
→ -15x = -45
→ 15x = 45
→ x = 3
Now, put the value of x in equation (1)
→ x + y = 11
→ 3 + y = 11
→ y = 11 - 3
→ y = 8
║Hence, the number of each types of notes are 3 and 8.║