Question

3 ducks and 4 chickens weigh 76kg. 4 ducks and 3 chickens weigh 78kg. All ducks weigh the same and all chickens weigh the same. What is the weight of 1 duck and 1 chicken?

Answer 1

The weight of 1 duck is 12 kg and weight of 1 chicken is 10 kg.

Answer 2

The weight of 1 duck = 12 Kg and weight of 1 chicken is 10 Kg.

Explanation:

Let the weight of one duck = x

Let the weight of one chicken = y

The weight of 3 ducks and 4 chicken is 76 kg

`\[=>3x+4y=76\]` ----- (1)

The weight of 4 ducks and 3 chicken is 78 kg

`\[=>4x+3y=78\]` ------- (2)

Let us multiply equation (1) by 4 and equation (2) by 3

`\[12x+16y=304\]` ------ (3)

`\[12x+9y=234\]` ------ (4)

Subtracting (3) and (4) :

`\[7y=70\]`

`\[y=10\]`

Substituting the value of y in (1):

`\[=>3x+ (4 * 10)=76\]`

`\[=>3x=76-40\]`

`\[=>x=12\]`

So the weight of 1 duck = 12 Kg and weight of 1 chicken is 10 Kg.