Question

A sum of ₹ 500 is in the form of denominations of ₹ 5 and ₹ 10. If the total number of notes is 90 find the number of notes of each denotation

Answer 1

Gɪᴠᴇɴ :-

• Total money = ₹500
• Total notes = 90
• Dimensions of notes = ₹5 and ₹10

ᴛᴏ ғɪɴᴅ :-

• Number of 5₹ notes
• Number of 10₹ notes

sᴏʟᴜᴛɪᴏɴ :-

Let number of ₹5 notes be x and ₹10 notes be y

then,

➢ According to 1st condition :-

• Total money = 500

➭ 5×(No of 5₹ note) + 10×(No of ₹10 notes) = 500

➭ 5(x) + 10(y) = 500

➭ 5x + 10y = 500

➭ 5(x + 2y) = 500

➭ x + 2y = 500/5

➭ x + 2y = 100

➭ x = 100 - 2y. --(1)

➢ According to 2nd condition :-

• Total number of notes = 90

• No of 5₹ notes + No of 10₹ notes = 90

➭ x + y = 90

➭ x = 90 - y. -(2)

From (1) and (2) , we get,

➭ 100 - 2y = 90 - y

➭ 100 - 90 = 2y - y

➭ y = 10

Put y = 10 in (2) , we get,

➭ x = 90 - y

➭ x = 90 - 10

➭ x = 80

Hence,

• Number of 5₹ notes = x = 80
• Number of 10₹ notes = y = 10

Answer 2

$\large\underline\bold{Question:-}$

A sum of ₹ 500 is in the form of denominations of ₹ 5 and ₹ 10. If the total number of notes is 90 find the number of notes of each denotation.

$\large\underline\bold{Answer:-}$

$\small\underline\bold{Given:-}$

$\sf\ Total\:money=Rs.500$

$\sf\ Total\: notes= 90$

$\sf\ Dimension\: of\: Notes=Rd.50\:and\:Rs.10$

$\small\underline\bold{To\:Find:-}$

$\sf\ No \:of\:notes=Rs.5$

$\sf\ No\:of\:notes=Rs.10$

$\small\underline\bold{Required\:Answer:-}$

$\sf\ Lets \:assume\: you\: have\: x\: notes\: of\: Rs 5 \:and \:y\: notes\: of \:Rs 10.$

$\sf\ So you have$

$\sf\ x+y =90$

$\sf\ And \:5x+10y=500.$

$\small\underline\bold{Puting\: x=10-y\: in\: 2nd\: equation}$

$\sf\ You have$

⟹$\sf\ 5(90-y)+10y=500$

⟹$\sf\ 450-5y+10y=500$

⟹$\sf\ 5y =500-450$

⟹$\sf\large\ y=\frac{50}{5} =10.$

⟹$\sf\ Hence\:x=90-10=80.$

$\sf\ So \:ans\: is$

†$\small\underline\bold\purple{80 \:of \:Rs. 5}$

†$\small\underline\bold\purple{10 \:notes\: of \:Rs10.}$