Question

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In a herd of camels one-fifth are male camels and are used for cart driving One third of camels are grazing in the field and three times the difference between these two numbers are drinking water at a stream. The remaining ten camels are lying due to illness. Find the number of camels in the herd.​

Answer 1

❥ $\huge\pink{answer}$

☞ solution

Then, x/5 are for cart driving, x/3 are grazing, 3*(x/3-x/5) are drinking water and 10 are ill. Therefore, the total number of camels in the herd is 150.

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Answer 2

Given :-

one - fifth are used for cart driving

one - third are grazing in the field

3 × ( one - third are grazing in the field minus one - fifth are used for cart driving ) are drinking water at a stream.

Number of camels remaining due to illnesses = 10

To find :-

Number of camels in the herd.

Solution:-

Let the total no of camels in the herd be

$x$

Now ,

Number of camels used for cart driving

$= \frac{1}{5} \: of \: x$

$= \frac{1}{5} \times x$

$\frac{x}{5}$

Number of camels grazing

$= \frac{1}{3} \: of \: x$

$= \frac{1}{3} \times x$

$= \frac{x}{3}$

Number of camels drinking water

= 3 × ( one - third are grazing in the field minus one - fifth are used for cart driving )

$= 3 \times ( \frac{x}{3} - \frac{x}{5} )$

$= 3 \times ( \frac{5x - 3x}{15} ) \: \: \: \: \: By \: LCM$

$= 3 \times ( \frac{2x}{15} )$

$= ( \frac{2x}{5} )$

$= \frac{2x}{5}$

Now as it is given in question

Number of camels remaining = 10

so therefore

⟹ When total camels - camels used for cart driving - Number of camels grazing - Number of camels drinking water will be equal to 10

$⟹ \: \frac{x}{1} - \frac{x}{5} - \frac{x}{3} - \frac{2x}{5} = 10$

$⟹ \frac{15x - 3x - 5x - 6x}{15} = 10\: \: \: \: \: By \: LCM$

$⟹ \frac{7x - 6x}{15} = 10$

$⟹ \frac{x}{15} = 10$

$⟹x = 10 \times 15$

$⟹x = 150$

Let's verify

Put x = 150 in the equation we get

$⟹ \: \frac{x}{1} - \frac{x}{5} - \frac{x}{3} - \frac{2x}{5} = 10$

$⟹ \: \frac{150}{1} - \frac{150}{5} - \frac{150}{3} - \frac{ 150×2 }{5} = 10$

$⟹ \: \frac{150}{1} - \frac{150}{5} - \frac{150}{3} - \frac{ 300 }{5} = 10$

$\frac{2250 - 450 - 750 - 900}{15} = 10 \: \: By \: LCM$

$\frac{150}{15} = 10$

$10 = 10$

L.H.S= RHS

Therefore verified

Hope it helps you