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

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Engineering graduate from NIT Calicut, Rank holder (#47) in State Entrance Examination.

number of rs 5 coins=x number of rupees 3 coins=3x since total number of coins is 160, number of rs 1 coins=160-3x-x=160-4x total cash in rupees=x*5+3x*2+(160-4x)*1=300 5x+6x+160-4x=300 7x=300-160=140 x=140/7=20 number of 5 rs coins=20 number of 2 rs coins=3x=3*20=60 number of 1 rs coins=160-4x=160-...
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number of rs 5 coins=x

number of rupees 3 coins=3x

since total number of coins is 160,

number of rs 1 coins=160-3x-x=160-4x

total cash in rupees=x*5+3x*2+(160-4x)*1=300

5x+6x+160-4x=300

7x=300-160=140

x=140/7=20

number of 5 rs coins=20

number of 2  rs coins=3x=3*20=60

number of 1 rs coins=160-4x=160-4*20=160-80=80

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Let the number of Rs 5 coins be x. Number of Rs 2 coins = 3 × Number of Rs 5 coins = 3x Number of Re 1 coins = 160 − (Number of coins of Rs 5 and of Rs 2) = 160 − (3x + x) = 160 − 4x Amount of Re 1 coins = Rs = Rs (160 − 4x) Amount of Rs 2 coins = Rs (2 × 3x)= Rs...
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Let the number of Rs 5 coins be x.

Number of Rs 2 coins = 3 × Number of Rs 5 coins = 3x

Number of Re 1 coins = 160 − (Number of coins of Rs 5 and of Rs 2)

= 160 − (3x + x) = 160 − 4x

Amount of Re 1 coins = Rs [1 × (160 − 4x)] = Rs (160 − 4x)

Amount of Rs 2 coins = Rs (2 × 3x)= Rs 6x

Amount of Rs 5 coins = Rs (5 × x) = Rs 5x

It is given that the total amount is Rs 300.

∴ 160 − 4x + 6x + 5x = 300

160 + 7x = 300

On transposing 160 to R.H.S, we obtain

7x = 300 − 160

7x = 140

On dividing both sides by 7, we obtain

x = 20

Number of Re 1 coins = 160 − 4x = 160 − 4 × 20 = 160 − 80 = 80

Number of Rs 2 coins = 3x = 3 × 20 = 60

Number of Rs 5 coins = x = 20

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