Question

15. I have a total of ₹300 in coins of denomination ₹1, ₹2 and ₹5. The number of ₹2 coins is 3 times the number of ₹5 coins. The total number of coins is 160. How many coins of each denomination are with me?

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Answer 1

Step-by-step explanation:

Given

15. I have a total of ₹300 in coins of denomination ₹1, ₹2 and ₹5. The number of ₹2 coins is 3 times the number of ₹5 coins. The total number of coins is 160. How many coins of each denomination are with me?

To Find

coins of each denomination are with me?

Solution

Refer To The Attachments

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Answer 2

${\large{\underline{\bf{\underline{Given\: : - }}}}}$

• ₹300 coins of denomination ₹1, ₹2 and ₹5.

• The number of ₹2 coins is 3 times the number of ₹5 coins.

• Total number of coins is 160

${\large{\underline{\bf{\underline{To \: find\: : - }}}}}$

• Number of coins in each denomination

${\large{\underline{\bf{\underline{Solution\: : - }}}}}$

➯ Suppose the number of 5 rupee coins be x

$\clubsuit\: \: \sf\bold{\green{According \: to \: the \: question\: :-}}$

➯Number of 2 rupee coins = 3 × number of 5 rupee coins

➯ Number of 2 rupee coins = 3 × x

➯ Number of 2 rupee coins = 3x

$\clubsuit\: \: \sf\bold{\pink{Further \: as \: per \: the \: question\: :-}}$

• Total number of coins = 160

∴ Number of one rupee coins + Number of two rupee coins + Number of five rupee coins = 160

⇒ Number of one rupee coins + 3x + x = 160

⇒ Number of one rupee coins + 4x = 160

∴ Number of one rupee coins = 160 - 4x

• Amount made by each denomination of coin :

➯ Amount made by 5 coins = 5(x) = 5x

➯ Amount made by 2 coins = 2(3x) = 6x

➯ Amount made by 1 coins = 1( 160 - 4x) = 160 - 4x

$\clubsuit\: \: \sf\bold{\red{We \: also \: have \: total \: amount = 300}}$

$➯ \sf \: 5 \times (x) +( 2)(3x) +( 1)(160 - 4x) = 300$

$➯\sf \: 5x + 6x + 160 - 4x = 300$

$➯ \sf \: 11x - 4x + 160 = 300$

$➯ \sf \: 7x + 160 = 300$

$➯7x = 300 - 160$

$➯\sf \: 7x = 140$

$➯ {\sf {x = {\dfrac{{\cancel{{140}}^{20}}}{{\cancel{{7}}^{1}}}}}}$

$\sf ➯\: x = 20$

∴ The number of five ruppe coins = x = 20

Number of two rupee coins = 3x

$\sf= 3 × 20$

$= 60$

Number of one rupee coins = 160 - 4x

$\sf= 160 - 4 \times 20$

$\sf = 160 - 80$

$\sf \: = 80$

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