Math, asked by asmitshaw939, 22 days ago

I have a total of Rs. 400 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?​

Answers

Answered by alamshahil819
1

Answer:

no. of Rs. 5 coins = 40

no. of rs. 2 coins = 80

no. of rs 1 coins = 40

Step-by-step explanation:

let no. of rs. 5 coins be x. since, 2( no. of rs. 2 coins) = no. of rs. 5 coins,

no. of rs. 2 coins = 2x.

and let no. of rs 1 coins be y.

total no. of coins = 160

therefore, x+ 2x+ y = 160

3x + y = 160...

.eq 1

+ y = 400

.eq 2

total amount = rs. 400

which implies, 5x + 2(2x) 9x+y=400...

(eq 2) - (eq 1),

9x + y = 400

3x + y = 160

6x = 240

x = 40

therefore, 2x = 80

sub value of x in eq 1,

3x + y = 160

120 + y = 160

y = 40

therefore,

no. of Rs. 5 coins = 40

no. of rs. 2 coins = 80

no. of rs 1 coins = 40

Answered by StarFighter
29

Answer:

Given :-

  • I have a total of Rs 400 in coins of denomination Re. 1, Rs. 2 and Rs. 5.
  • The numbers of Rs. 2 coins is 3 times the number of Rs. 5 coins.
  • The total number of coins is 160.

To Find :-

  • How many coins of each denomination are with me.

Solution :-

Let,

\mapsto \bf Number\: of\: Rs\: 5\: coins =\: x

Given that :

\bigstar The number of Rs. 2 coins is 3 times the number of Rs. 5 coins.

\mapsto \bf Number\: of\: Rs\: 2\: coins =\: 3x

Now,

\mapsto \sf Number\: of\: Re\: 1\: coins =\: 160 - (x + 3x)\\

\mapsto \bf Number\: of\: Re\: 1\: coins =\: 160 - 4x\\

According to the question :

\implies \sf (5 \times x) + (2 \times 3x) + (160 - 4x) =\: 400\\

\implies \sf 5x + 6x + 160 - 4x =\: 400

\implies \sf 5x + 6x - 4x + 160 =\: 400

\implies \sf 11x - 4x + 160 =\: 400

\implies \sf 7x + 160 =\: 400

\implies \sf 7x =\: 400 - 160

\implies \sf 7x =\: 240

\implies \sf x =\: \dfrac{240}{7}

\implies \sf\bold{\purple{x =\: 34}}

Hence, the required coins are :

Number of Rs 5 coins :-

➳ x

Rs 34

Number of Rs 2 coins :-

➳ 3x

➳ 3(34)

➳ 3 × 34

Rs 102

Number of Re 1 coins :-

➳ 160 - 4x

➳ 160 - 4(34)

➳ 160 - 136

Rs 24

\therefore The number of Re 1 coins is Rs 24, number of Rs 2 coins is Rs 102 and the number of Rs 5 coins is Rs 34 .

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