Question

a factory makes orange paint by mixing red paint and yellow paint in the ratio 7:2 .The factory makes 2700 liters of orange paint everyday. how many liters of yellow paint does the factory use every day
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Answer 1

Answer :-

$\: \\ \: \boxed{\boxed{\rm{\mapsto \: \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of Ratios of the values has been used. We are given that the red and yellow paint are in the ratio of 7:2 . This means that there will be a constant x by which these both should be multiplied to find the answer. Let's find that.

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★ Formula Used :-

$\: \\ \large{\boxed{\boxed{\sf{7x \: \: + \: \: 2x \: \: = \: \: \bf{2700 \: \: Litres}}}}}$

$\: \\ \large{\sf{Quantity\:of\:Each\:Paint_{(red \: or \: yellow)}\:\:Used \: = \: \bf{Ratio\:part\:of\: that\:Colour\: \times\:The\:Value\:of\:x}}}$

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★ Question :-

A factory makes orange paint by mixing red paint and yellow paint in the ratio 7:2 .The factory makes 2700 litres of orange paint everyday. How many litres of yellow paint does the factory use every day .

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★ Solution :-

Given,

» Ratio of red paint to yellow paint to manufacture orange paint  = 7  :  2

» Capacity of Orange Paint made by factory = 2700 Litres

• Let the constant by which 7 and 2 should ve multiplied to tet original value be 'x'. Then,

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~ For the value of 'x' :-

$\: \\ \qquad \large{\sf{:\longrightarrow \: \: \: (Quantity \: of \: Red \: paint)_{(in \: Litres)}\: \: + \: \: (Quantity \: \: Yellow \: Paint)_{(in \: litres)} \: = \: \: \bf{Total \: \: Quantity}}}$

$\: \\ \qquad \large{\sf{:\longrightarrow \: \: \: 7x \: Litre\: \: + \: \: 2x \: Litre\: \: = \: \: \bf{2700 \: \: Litres}}}$

$\: \\ \qquad \large{\sf{:\longrightarrow \: \: \: 9x \: Litre\: \: \: = \: \: \bf{2700 \: \: Litres}}}$

$\: \\ \qquad \large{\sf{:\longrightarrow \: \: \: x \: \: \: \: = \: \: \tt{\dfrac{\cancel{2700} \: \: \cancel{Litres}}{\cancel{9} \: \: \cancel{Litres}}} \: \: = \: \: \underline{\underline{\bf{300}}}}}$

$\: \\ \large{\boxed{\boxed{\tt{Hence \;\: the \:\; value \:\; of \:\; x \:\; = \:\; \bf{300}}}}}$

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~ For the Quantity of Each Paint :-

$\: \\ \large{\sf{:\Longrightarrow \: \: \: Quantity \: of \: Each \: Paint_{(red \: or \: yellow)} \: Used \: = \: \bf{Ratio \: part \: of \: that \: Colour \: \times \: The \: Value \: of \: x}}}$

$\: \\ \qquad \large{\sf{:\Longrightarrow \: \: \: Quantity \: of \: Yellow \: Paint \: Used \: = \: \bf{2\; Litres \: \times \: 300 \: \: = \: \: \underline{\underline{600 \: \: Litres}}}}}$

$\: \\ \qquad {\sf{:\Longrightarrow \: \: \: Quantity \: of \: Red \: Paint \: Used \: = \: \bf{7\; Litres \: \times \: 300 \: \: = \: \: \underline{\underline{2100 \: \: Litres}}}}}$

$\: \\ \large{\underline{\underline{\rm{\mapsto \: \: \: Thus, \: quantity \: of \: yellow \: paint \: used \: by \: factory \: everyday \: is \: \: \boxed{\bf{600 \: \: Litres}}}}}}$

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$\: \\ \qquad \large{\underbrace{\underbrace{\sf{Confused? \: \: Don't \: \: worry \: \: let's \: \: verify \: \: it \: \: :-}}}}$

For verifying, we need to simply apply the value we got into the equation we formed. Then,

=> 7x Litres + 2x Litres = 2700 Litres

=> 7(300) Litres + 2(300) Litres = 2700 Litres

=> 2100 Litres + 600 Litres = 2700 Litres

=> 2700 Litres = 2700 Litres

Clearly, LHS = RHS.

Here the condition is satisfied by the value of x. So our answer is correct.

Hence, Verified.

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Answer 2

Given,

a factory makes orange paint by mixing red paint and yellow paint in the ratio 7:2 .The factory makes 2700 liters of orange paint everyday.

To find :

How many liters of yellow paint does the factory use every day .

Solution :

Let the number of liters of red and yellow paint be 7n and 2n

Atq,

⇒ 7n + 2n = 2700

⇒ 9n = 2700

⇒ n = 2700/9

⇒ n = 300 liters

Now number of liters of red and yellow paint :

∴ Number of liters of red paint = 7n = 7(300) = 2100 l

∴ Number of liters of yellow paint = 2n = 2(300) = 600 l

Therefore,

600 liters of yellow paint the factory uses everyday.