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One fourth of a herd of a herd of camel was seen in the forest. One third of the herd had gone to mountain and the remaining 15 camels were seen on the bank of a river . Find the total number of camels in the herd.



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Answer 1

☆ Question :

• One fourth of camels of herd were seen in the forest, one third of the camels had gone to mountains and the remaining 15 camels were seen on the bank of the river. Find the total number of camels in the herd.

☆ Answer :

• Total number of camels in the herd = 36

☆ Explanation :

Given :

• One fourth of camels of herd were seen in the forest.

• One third of the camels had gone to mountains.

• 15 camels were seen on the bank of river.

To Find :

• Total number of camels in the herd?

Solution :

• Let the total number of camels in the herd be 'x'.

According to the question,

• ¼ of camels of a herd were seen in the forest.

• ⅓ of camels of the herd had gone to mountains.

• 15 camels were seen on the bank of the river.

Therefore,

$\implies \:\frac{1}{4} x \: + \frac{1}{3} x \: + 15 \: = \: x$

$\implies \: \frac{x}{4} \: + \: \frac{x}{3} \: + \: 15 \: = \: x$

$\implies \: \frac{3x + 4x}{12} \: + \: 15 \: = \: x$

$\implies \: \frac{7x}{12} \: + \: 15 \: = \: x$

$\implies \: \frac{7x + 180}{12} \: = \: x$

$\implies \: 7x \: + \: 180 \: = x \times 12$

$\implies \: 7x \: + \: 180 \: = \: 12x$

$\implies \: 180 \: = \: 12x \: - \: 7x$

$\implies \: 180 \: = \: 5x$

$\implies \: \frac{180}{5} \: = \: x$

$\implies \cancel \frac{180}{5} \: = \: x$

$\implies \: 36 \: = \: x$

$\green\implies \green{x \: = \: 36}$

☆ Let's Verify :

We know that,

$\frac{1}{4}x \: + \: \frac{1}{3}x \: + \: 15 \: = \: x$

Now,

By putting the value 'x' in this equation,

We get,

$(\frac{1}{4} \times 36) \: + ( \frac{1}{3} \times 36) \: + 15 \: = 36$

$\implies \: \frac{36}{4} + \frac{36}{3} + 15 = 36$

$\implies \: \frac{3 \times 36 + 4 \times 36}{12} + 15 = 36$

$\implies \: \frac{108 + 144}{12} + 15 = 36$

$\implies \: \frac{252}{12} \: + 15 \: = \: 36$

$\implies \: \frac{252 + 180}{12} \: = \: 36$

$\implies \: \frac{432}{12} \: = \: 36$

$\implies \: 36 \: = \: 36$

$\blue\implies \blue{LHS \: = \: RHS}$

Hence Verified.

Answer 2

Let the total number of camels in the herd be 'x'.

According to the question,

¼ of camels of a herd were seen in the forest.

⅓ of camels of the herd had gone to mountains.

15 camels were seen on the bank of the river.

Therefore,

1/4x + 1/3x + 15 = x

=> 7x + 180/12 = x

=> 180 = 12x - 7x

=> 180 = 5x

=> x = 36