a total of 90 currency notes, consisting only of rupees 5 and Rupees 10 denominations, amount to rupeese 500.find the number of notes in each denomination.
Answers
Answer:
Let the number of Rs. 5 currencies be denoted as 'x' and Rs. 10 currencies be denoted as y.
According to the question,
⇒ x + y = 90
Also, it is given that total amount is Rs. 500. Therefore it is given as:
⇒ 5x + 10y = Rs. 500
⇒ x + 2y = 100
Solving both the equations we get,
⇒ x + 2y = 100
⇒ x = 100 - 2y
Substituting this in the first equation we get,
⇒ ( 100 - 2y ) + y = 90
⇒ 100 - y = 90
⇒ y = 100 - 90
⇒ y = 10
Therefore x can be found out as:
⇒ x = 100 -2y
⇒ x = 100 - 2 ( 10 )
⇒ x = 100 - 20
⇒ x = 80
Therefore number of notes of Rs. 5 denominations were 80 and that of Rs. 10 were 10.
The number of 5 rupees notes is 80.
The number of 10 rupees notes is 10.
Explanation:
Let, the number of 5 rupees notes be, "n".
∴ The number of 10 rupees notes = (90-n)
The 5 rupees notes together make an amount of_
(n×5)
= 5n
The 10 rupees notes together make an amount of _
(90-n)×10
= 900-10n
According to the problem,
5n+(900-10n) = 500
⇒ 5n-10n +900 = 500
⇒ -5n = 500-900
⇒ -5n = -400
⇒ 5n = 400
⇒ n = 400/5
⇒ n = 80
∴ The number of 5 rupees notes is 80.
∴ The number of 10 rupees notes is = (90-80)
= 10
Check whether the calculation is right or wrong:
The number of 5 rupees notes = 80.
The number of 10 rupees notes = 10.
∴ Total number of notes = (80+10)
= 90.
The 5 rupees notes together amounts to_
Rs. (80×5)
= Rs. 400
The 10 rupees notes together amounts to_
Rs. (10×10)
= Rs. 100
∴ The total sum of money is_
Rs. (400+100)
= Rs.500.