A sum of rs 370 is in the form of denominations of rs 10 and rs 50. if the number of 10 rupee notes is one more that of 50 rupee notes,find the number of notes of each type
Answers
no. of 50rs notes =y
so, 10x + 50y = 370
given , x = y+1
now , 10(y+1) + 50y = 370.
60y = 360.
y = 6 notes of 50rs.
x= y+1 = 7 notes of 10rs.
Answer:
SOLUTION :
Let the number of 50 rupee notes = a
Then the number of 10 rupee note = (a+1)
(as according to the question the number of 10 rupee notes is one than that of 50 rupee)
Value of 50 rupee notes = 50 × a
Value of 10 rupee note = 10(a+1)
Total money = 50 × a + 10(a+1)
= 50a + 10a +10
Now,
50a + 10a + 10 = 370
[as the piggy bank contains total money Rs 370]
⇒ 60a + 10 = 370
⇒ 60a = 370 - 10
[transporting 10 to RHS]
⇒ 60a = 360
⇒ a = 360 ÷ 60
⇒ a = 6
Therefore,
Number of 50 rupee note = a = 6
Number of 10 rupee notes = (a+1) = 6+1 = 7
CHECK :
Total money = 50 × 6 + 10 × 7 = 300 + 70 = Rs 370
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Given
Total money =370
let
No. of 10rupeenotes=x+1
no. of 50rupee notes=x
value
50rupee notes=50(x)
10rupee notes =10(x+1)
=10x+10
Final. equation
10x+10+50x=370
60x=370-10
60x=360
x=360/60
x=60
Conclusion
number. of 50rupee notes=6
number of 10rupee notes =6+1=7