Question

A bag contains $510 in the form of 50 p, 25 p and 20 p coins in the ratio 2 : 3 : 4. Find the number of coins of each type. ​

Answer 1

Given :

• Total amount of money is $510
• Money in form 50p, 25p and 20p
• Money in ratio 2 : 3 : 4

To find :

• the numbers of coins of each type

Solution :

Let the number of 50 p, 25 p and 20 p coins be

• 2x, 3x and 4x.

Then,

$\tt \to(2x \times \cancel \frac{50}{100} )+ (3x \times \cancel \frac{25}{100}) +( 4x \times \cancel \frac{20}{100} ) = 510$

$\tt \to( \cancel2x \times \frac{1}{ \cancel2} ) + (3x \times \frac{1}{4} ) + (4x \times \frac{1}{5}) = 510$

$\tt \to x + \frac{3x}{4} + \frac{4x}{5} = 510$

$\tt \to \frac{20x + 15x + 16x}{20} = 510$

$\tt \to \frac{51x}{20} = 510$

$\tt \to \: x = \cancel{510} \times \frac{20}{ \cancel{51} }$

$\tt \to \: x = 200$

Now,

• 2x = 2(200) = 400
• 3x = 3(200) = 600
• 4x = 4(200) = 800

Therefore, number of 50 p coins, 25 p coins and 20 p coins are $\tt{\red{<strong>400, 600, 800</strong>}}$ respectively.

Answer 2

$\large\underline{ \underline{ \sf \maltese{ \: Question⤵}}}$

A bag contains $510 in the form of 50 p, 25 p and 20 p coins in the ratio 2 : 3 : 4. Find the number of coins of each type.

✴ Solution ⬇

Let the number of 50 p, 25 p and 20 p coins be

2x, 3x and 4x.

Then,

$\tt \to(2x \times \cancel \frac{50}{100} )+ (3x \times \cancel \frac{25}{100}) +( 4x \times \cancel \frac{20}{100} ) = 510$

$\tt \to( \cancel2x \times \frac{1}{ \cancel2} ) + (3x \times \frac{1}{4} ) + (4x \times \frac{1}{5}) = 510$

$\tt \to x + \frac{3x}{4} + \frac{4x}{5} = 510$

$\tt \to \frac{20x + 15x + 16x}{20} = 510$

$\tt \to \frac{51x}{20} = 510$

$\tt \to \: x = \cancel{510} \times \frac{20}{ \cancel{51}}$

$\tt \to \: x = 200$

Now,

2x = 2(200) = 400

3x = 3(200) = 600

4x = 4(200) = 800

Therefore, number of 50 p coins, 25 p coins and 20 p coins are $\tt{\blue{400, 600, 800}}$ respectively.

Thank you.