Question

Mahesh picked up Rs 6100 from an ATM, all in denominations of Rs 100 and Rs 500. There were 45 notes in all. Which of the following pairs of equations can be used to find the number of 100-rupee and 500-rupee notes? (Note: x represents 100-rupee note and y represents 500-rupee note)

Answer 1

Gɪᴠᴇɴ :-

• Total money = 6100
• Dimensions of notes = ₹100 & ₹500
• Total number of notes = 45

ᴛᴏ ғɪɴᴅ :-

Number of :-

• ₹100 notes
• ₹500 notes

sᴏʟᴜᴛɪᴏɴ :-

Let number of ₹100 notes be x and ₹500 be y

then,

According to 1st condition :-

• Total money = 6100

➭ 100(x) + 500(y) = 6100

➭ 100x + 500y = 6100

➭ 100 (x + 5y) = 6100

➭ x + 5y = 6100/100

➭ x + 5y = 61

➭ x = 61 - 5y. --(1)

According to 2nd condition :-

• Total number of notes = 45

➭ x + y = 45

➭ x = 45 - y. --(2)

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

➭ 61 - 5y = 45 - y

➭ 61 - 45 = 5y - y

➭ 16 = 4y

➭ y = 16/4

➭ y = 4

Put y = 4 in (2) , we get,

➭ x = 45 - y

➭ x = 45 - 4

➭ x = 41

Hence,

• Number of 100₹ notes = x = 41
• Number of 500₹ notes = y = 4

Answer 2

Answer:

${\bf{\orange{GIVEN :-}}}$

Total money = 6100

Dimensions of notes = ₹100 & ₹500

Total number of notes = 45

${\bf{\orange{TO FIND:-}}}$ᴛᴏ

₹100 notes

₹500 notes

${\bf{\orange{SOLUTION:-}}}$

Let number of ₹100 notes be x and ₹500 be y

then,

According to 1st condition :-

Total money = 6100

➡️100(x) + 500(y) = 6100

➡️ 100x + 500y = 6100

➡️ 100 (x + 5y) = 6100

➡️ x + 5y = 6100/100

➡️ x + 5y = 61

➡️ x = 61 - 5y. --(1)

According to 2nd condition :-

Total number of notes = 45

➡️x + y = 45

➡️ x = 45 - y. --(2)

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

➡️ 61 - 5y = 45 - y

➡️ 61 - 45 = 5y - y

➡️ 16 = 4y

➡️ y = 16/4

➡️ y = 4

Put y = 4 in (2) , we get,

➡️ x = 45 - y

➡️ x = 45 - 4

➡️x = 41

Hence,

• Number of 100₹ notes = x = 41
• Number of 500₹ notes = y = 4