Gourav has a total of Rs.590 as currency notes in the denominations of Rs. 50, Rs. 20 and Rs. 10. The ratio of the number of Rs. 50 notes and Rs. 20 notes is 3:5. If she has a total of 25 notes, how many notes of each denomination he has?
Pls help me solve this question
Answers
Step-by-step explanation:
Given Gourav has 590 Rupees
RS50,20&10 are there ⇒ Total 25 notes
Rs50&Rs20 ⇒3:5
Notes of Rs50=3x
Notes of Rs20=5x
Notes of Rs10=25−(3x+5x)=25−8x.
Amount in 50 Rupee notes ⇒50×3x=150x
Amount in 20 Rupee notes ⇒20×5x=100x.
Amount in 10 Rupee notes ⇒10(25−8x)=250−80x
Total Amount =590
⇒150x+100x+250−80x=590
⇒250−80x=590−250
⇒170x=340
∴x=2
So Gaurav has
Notes of Rs.50=3(2)=6i.e;150(2)=300Rs.
Notes of Rs.20=5(2)=10i.e;100(2)=200Rs.
Notes of Rs.10=25−8(2)=9i.e;=90Rs
Hope it helps.
Given:-
- Total of currency notes Gourav has = Rs. 590
- He has domination of Rs. 50, Rs. 20, Rs. 10.
- Ratio of the number of Rs. 50 and Rs. 20 notes = 3 : 5
- Total number of notes he has = 25
To Find:-
- Number of notes of each domination.
Solution:-
Let the number of Rs. 10 notes be y, Rs. 50 notes be 3x and Rs. 20 notes be 5x.
According to the question,
3x + 5x + y = 25
8x + y = 25
y = 25 - 8x •••(1)
50(3x) + 20(5x) + 10(y) = Rs. 590
150x + 100x + 10y = 590
250x + 10y = 590 •••(2)
Substituting the value of y (equation 1) in equation (2), we get,
250x + 10(25 - 8x) = 590
250x + 250 - 80x = 590
170x = 590 - 250 = 340
x = 340/170
x = 2
Therefore,
Domination of Rs. 10 notes = y = 25 - 8x = 25 - 8(2) = 25 - 16 = 9
Domination of Rs. 20 notes = 5x = 5 × 2 = 10
Domination of Rs. 50 notes = 3x = 3 × 2 = 6
Verification:-
RHS = 50 × 3x + 20 × 5x + 10 × y
= 50 × 6 + 20 × 10 + 10 × 9
= 300 + 200 + 90
= 590 = LHS
Thus, RHS = LHS
Hence, verified!