Question

Anil gave his son Rs 920 in coins of denominations Rs 2, Rs 5, and Rs 10. The number of Rs 5 coins is two times the number of Rs 2 coins. If the total number of coins is 200, find the number of coins of each denomination given to his son.

Answer 1

Answer:

The number of Rs 5 coins is two times the number of Rs 2 coins. If the total number of coins is 200, find the number of ...

Answer 2

ɢɪᴠᴇɴ :-

Anil gave his son Rs 920 in coins of denominations Rs 2, Rs 5, and Rs 10. The number of Rs 5 coins is two times the number of Rs 2 coins. If the total number of coins is 200.

ᴛᴏ ғɪɴᴅ :-

Number of :-

• 2 rupee coins
• 5 rupee coins
• 10 rupee coins

sᴏʟᴜᴛɪᴏɴ :-

Let the number of 2 rupee coin be x and 10 rupee coin be y

then,

➥ Number of 5-rupee coins = 2 × (No of 2Rs coin)

➥ No of 5 rupee coins = 2x

Now,

➤ According to 1st condition :-

• Total money = 920₹

• 2(No of ₹2 coin) + 5(No of ₹5 coin) + 10(No of 10₹ coin) = 920

➭ 2(x) + 5(2x) + 10(y) = 920

➭ 2x + 10x + 10y = 920

➭ 12x + 10y = 920

➭ 2(6x + 5y) = 920

➭ 6x + 5y = 920/2

➦ 6x + 5y = 460. ---(1)

➤ According to 2nd condition :-

• Total number of coins = 200

• No of ( 2₹ coin + 5₹ coin + 10₹ coin) = 200

➭ x + 2x + y = 200

➭ 3x + y = 200

➦ y = 200 - 3x. --(2)

Put the value of (2) in (1) , we get,

➭ 6x + 5y = 460

➭ 6x + 5(200 - 3x) = 460. --(from -1)

➭ 6x + 1000 - 15x = 460

➭ -9x = 460 - 1000

➭ -9x = -540

➭ x = -540/-9

➦ x = 60

Put x = 60 in (2) , we get,

➭ y = 200 - 3x

➭ y = 200 - 3×60

➭ y = 200 - 180

➦ y = 20

Hence,

Number of :-

• 2 rupee coin = x = 60
• 5 rupee coin = 2x = 2×60 =120
• 10 rupee coin = y = 20