Question

A sum of rs 530 is in the form of denominations of rs 5 and re 10. If the total number of notes be 79, find the number of each type of notes.​

Answer 1

ɢɪᴠᴇɴ :-

A sum of rs 530 is in the form of denominations of rs 5 and re 10. The total number of notes is 79.

ᴛᴏ ғɪɴᴅ :-

Number of :-

• 5₹ notes
• 10₹ notes

sᴏʟᴜᴛɪᴏɴ :-

Let number of 5 - rupee note be x and 10 - rupee note be y

then,

✞ According to 1st condition :-

• Total money = 530

• No of 5₹ notes + No of 10₹ note = 530

↦ 5x + 10y = 530

↦ 5(x + 2y) = 530

↦ x+ 2y = 530/5

↦ x + 2y = 106

➦ x = 106 - 2y. --(1)

✞ According to 2nd condition :-

• Total number of notes = 79

• No of 5₹ notes + No of 10₹ notes = 79

↦ x + y = 79

➦ x = 79 - y. --(2)

Now,

From (1) and (2) , we get

↦ 106 - 2y = 79 - y

↦ -2y + y = 79 - 106

↦ -y = -27

➦ y = 27

Put y = 27 in (2) , we get,

↦ x = 79 - y

↦ x = 79 - 27

➦ x = 52

Hence,

• No of 5₹ notes = x = 52
• No of 10₹ notes = y = 27

Answer 2

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