Question

In a box there are 378 coins in one rupee,50 Paisa, and 25 Paisa coins If the ratio of their values be 13:11:7, find the number of each kind of coin in the box.

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Answer 1

Let's assume that the number of 1 rupee coins in the box is x, the number of 50 paisa coins is y, and the number of 25 paisa coins is z.

From the problem, we know that the ratio of the values of these coins is 13:11:7. We can write this as:

13x = 11y + 7z

We also know that there are 378 coins in the box. We can write this as:

x + y + z = 378

We have two equations and two unknowns, so we can solve for x, y, and z.

First, let's solve for z in terms of x and y:

z = 378 - x - y

Now, let's substitute this equation into the first equation:

13x = 11y + 7(378 - x - y)

Simplifying and solving for y, we get:

y = 126

Now, we can substitute this value of y into either of the two equations to solve for x and z. Let's use the equation x + y + z = 378:

x + 126 + z = 378

z = 252 - x

Now, we can substitute this equation into the equation 13x = 11y + 7z:

13x = 11(126) + 7(252 - x)

Simplifying and solving for x, we get:

x = 84

Finally, we can use the equations z = 252 - x and y = 126 to find z:

z = 168

Therefore, there are 84 1-rupee coins, 126 50-paisa coins, and 168 25-paisa coins in the box.