Question

100 rupees 100 animals.1 elephant -20,1 horse-1,4 goat -1.

Answer 1

Given:

Cost of 1 elephant = Rs. 20

Cost of 1 horse = Rs. 1

Cost of 4 goats = Rs. 1

⇒ Cost of 1 goat = Rs. 1/4

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To find:

Number of elephant = ?

Number of horses = ?

Number of goats = ?

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Consideration:

Number of elephants = x

Number of horses = y

Number of goats = z

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Now we proceed to solve the given problem:

• For the quantity 100: x + y + z = 100
• For the money Rs. 100: 20x + y + z/4 = 100

We cannot solve two equations with three unknown variables. This is why we take z = 4, 8, 12, ..., 96, since x, y, z must give integral values and none of x, y, z is zero (0).

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When z = 4:

We have the set of equations,

• x + y = 96
• 20x + y = 99

On subtraction, 19x = 3 or, x = 3/19, a non-integral value.

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When z = 8:

We have the set of equations,

• x + y = 92
• 20x + y = 98

On subtraction, 19x = 6 or, x = 6/19, a non-integral value.

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When z = 12:

We have the set of equations,

• x + y = 88
• 20x + y = 97

On subtraction, 19x = 9 or, x = 9/19, a non-integral value.

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We see that in our solutions for x, 19 is coming in the denominator and the difference of the two consecutive fractions give 3 in its numerator.

Now we take z = 4 * multiplies of 19.

Then z = 76 ( this is the only possible value of z = 4 * multiplies of 19 ).

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When z = 76:

We have the set of equations,

• x + y = 24
• 20x + y = 81

On subtraction, 19x = 57 or, x = 3, an integral value.

Then y = 21 and z = 76.

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Answer:

• Number of elephants = 3
• Number of horses = 21
• Number of goats = 76

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Confirmation:

Total quantity = 3 + 21 + 76 = 100

Total cost = Rs. 20 (3) + 21 (1) + 76 (1/4) = Rs. 100

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Answer 2

3 elephants + 21 horses + 76 goats = Rs. 100

Step-by-step explanation:

Given: 1 elephant -20, 1 horse-1, 4 goat -1.

100 rupees 100 animals

Solution:

Let x be elephant, y be horse, and z be goat.

So we have x + y + z = 100 ------(1)

And 20x + y + z/4 =  100 -----(2)

Since z is a fraction, we have to take multiples of 4 for the value of z. That would be 4, 8, 12....96.

We can find the values by substituting any value for z on a trial basis.

The correct answer will be such that x, y and z all are integers as animals can't be fractions.

Upon solving, we find that z = 76 yields integer values for x, y and z.

Assuming z = 76, equations 1 and 2 will become:

x + y + 76 = 100

x + y = 24 ------(3)

20x + y +76/4 = 100

20x + y + 19 = 100

20x + y = 81 ----(4)

subtracting 3 from 4, we get:

19x = 57

Therefore x = 3.

Substituting x and z in equation 1, we get:

3 + y + 76 = 100

y = 21

Hence solved.

3 elephants + 21 horses + 76 goats = Rs. 100