Question

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?​

Answer 1

Answer:

24 Silver Coins

Step-by-step explanation:

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

Then,

$\frac{x}{y}$ = $\frac{5}{6}$        ----------- (i)

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

$\frac{x+5}{y-4}$ = $\frac{5}{4}$

=> x+5 = $\frac{5(y-4)}{4}$

=> x + 5 = $\frac{5y-20}{4}$

=> x  = $\frac{5y-20}{4}$ - 5

=> x =  $\frac{5y-20 - 20}{4}$

=> x =  $\frac{5y - 40}{4}$   -------------( ii )

Rearranging Equation (i),

x = 5y/6 --------(iii)

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

$\frac{5y}{6}$ =  $\frac{5y - 40}{4}$

5y =  $\frac{5y - 40}{4}$ x $\frac{6}{1}$

5y =  $\frac{3(5y - 40)}{2}$

10y = 15y - 120

15y - 10y  = 120

5y = 120

y = 24

Substituting y value in equation (i),

$\frac{x}{24}$ = $\frac{5}{6}$  

x = $\frac{5 (24)}{6}$

x = 5 x 4

x = 20

∴ There are 20 gold coins and 24 silver coins

Answer 2

Answer:

24 coins

Step-by-step explanation: