roni has rs 486 in coins of denominations one rupee, two rupees and five rupees. the total number of coins is 200. the ratio of the number of two-rupees coins and five rupees coins is 5:2. find the number of coins of each denomination
Answers
Solution -
Let the no. of ₹2 coins be 5x
The no. of ₹5 coins be 2x
The no. of ₹1 coins be 200 - (5x + 2x)
= 200 - 7x
Amount from,
₹2 coins = ₹(2 × 5x) = ₹10x
₹5 coins = ₹(5 × 2x) = ₹10x
₹1 coins = ₹(1 × 200 - 7x)
= ₹ 200 - 7x
According to Question,
Total amount = ₹486
⇒ 10x + 10x + 200 - 7x = 486
⇒ 13x = 486 - 200 = 286
⇒ x = 286/13
⇒ x = 22
Number of coins -
From ₹1 = 200 - 7x = 200 - 7(22)
= 200 - 154 = 46
From ₹2 = 5x = 5(22) = 110
From ₹5 = 2x = 2(22) = 44
∴ Number of coins from ₹1 is 110, from ₹2 is 110 and from₹5 is 44
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neerajomer
neerajomer
04.08.2018
Math
Secondary School
answered
roni has rs 486 in coins of denominations one rupee, two rupees and five rupees. the total number of coins is 200. the ratio of the number of two-rupees coins and five rupees coins is 5:2. find the number of coins of each denomination
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Solution -
Let the no. of ₹2 coins be 5x
The no. of ₹5 coins be 2x
The no. of ₹1 coins be 200 - (5x + 2x)
= 200 - 7x
Amount from,
₹2 coins = ₹(2 × 5x) = ₹10x
₹5 coins = ₹(5 × 2x) = ₹10x
₹1 coins = ₹(1 × 200 - 7x)
= ₹ 200 - 7x
According to Question,
Total amount = ₹486
⇒ 10x + 10x + 200 - 7x = 486
⇒ 13x = 486 - 200 = 286
⇒ x = 286/13
⇒ x = 22
Number of coins -
From ₹1 = 200 - 7x = 200 - 7(22)
= 200 - 154 = 46
From ₹2 = 5x = 5(22) = 110
From ₹5 = 2x = 2(22) = 44
∴ Number of coins from ₹1 is 110, from ₹2 is 110 and from₹5 is 44.