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Some gold and silver coins are kept in a box in the ratio of 5:6. If 5 gold coins are added and 4 silver coins are
remo

By Lydia

Some gold and silver coins are kept in a box in the ratio of 5:6. If 5 gold coins are added and 4 silver coins are
removed from the box, the ratio becomes 5:4. What is the number of silver coins at the beginning?​

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Lydia

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2 thoughts on “<br />Some gold and silver coins are kept in a box in the ratio of 5:6. If 5 gold coins are added and 4 silver coins are<br />remo”

  2. Answer:

    24 Silver Coins

    Step-by-step explanation:

    Let x and y be the number of gold coins and silver coins respectively

    Then,

    [tex]\frac{x}{y}[/tex] = [tex]\frac{5}{6}[/tex] ———– (i)

    When 5 gold coins were added and 4 coins were removed, then ratio becomes 5:4,

    [tex]\frac{x+5}{y-4}[/tex] = [tex]\frac{5}{4}[/tex]

    => x+5 = [tex]\frac{5(y-4)}{4}[/tex]

    => x + 5 = [tex]\frac{5y-20}{4}[/tex]

    => x = [tex]\frac{5y-20}{4}[/tex] – 5

    => x = [tex]\frac{5y-20 – 20}{4}[/tex]

    => x = [tex]\frac{5y – 40}{4}[/tex] ————-( ii )

    Rearranging Equation (i),

    x = 5y/6 ——–(iii)

    Substituting value of x from (iii) in (ii),

    [tex]\frac{5y}{6}[/tex] = [tex]\frac{5y – 40}{4}[/tex]

    5y = [tex]\frac{5y – 40}{4}[/tex] x [tex]\frac{6}{1}[/tex]

    5y = [tex]\frac{3(5y – 40)}{2}[/tex]

    10y = 15y – 120

    15y – 10y = 120

    5y = 120

    y = 24

    Substituting y value in equation (i),

    [tex]\frac{x}{24}[/tex] = [tex]\frac{5}{6}[/tex]

    x = [tex]\frac{5 (24)}{6}[/tex]

    x = 5 x 4

    x = 20

    ∴ There are 20 gold coins and 24 silver coins

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