A bag contains coins of one rupee, two rupee & five rupees. The total money in the bag is Rs. 120. If the total number of one rupee and two rupee coins are 35 and in ratio of coins is 2 : 5. Find the probability of getting a 5 rupee coin if a coin is randomly picked from the bag?a)2/7b)5/7c)5/47d)12/47Correct answer is option 'D'. Can you explain this answer?

Question

Answer

, and five rupee denominations. The total number of coins in the bag is 100, and the total value of the coins is 200 rupees. How many coins of each denomination are in the bag?

Let's assume the number of one rupee coins is x, the number of two rupee coins is y, and the number of five rupee coins is z.

From the problem, we know the following equations:

1. x + y + z = 100 (equation 1) - The total number of coins is 100.
2. 1x + 2y + 5z = 200 (equation 2) - The total value of the coins is 200 rupees.

We can solve this system of equations to find the values of x, y, and z.

Multiplying equation 1 by 2, we get:
2x + 2y + 2z = 200 (equation 3)

Subtracting equation 2 from equation 3, we get:
(2x + 2y + 2z) - (1x + 2y + 5z) = 200 - 200
x - 3z = 0 (equation 4)

Substituting equation 4 into equation 1, we get:
x + y + 3x = 100
4x + y = 100 (equation 5)

Now we have two equations:
x - 3z = 0 (equation 4)
4x + y = 100 (equation 5)

To solve these equations, we can use substitution or elimination method.

Let's solve by substitution:
From equation 4, we have: x = 3z
Substituting this into equation 5, we get:
4(3z) + y = 100
12z + y = 100 (equation 6)

We now have two equations:
12z + y = 100 (equation 6)
x = 3z (equation 4)

We can solve equation 6 for y:
y = 100 - 12z

Substituting this into equation 4, we get:
x = 3z

Substituting the values of x and y into equation 1, we get:
3z + (100 - 12z) + z = 100
4z + 100 - 12z = 100
-8z = 0
z = 0

If z = 0, then x = 3z = 3(0) = 0

Substituting z = 0 into equation 6, we get:
y = 100 - 12(0)
y = 100

Therefore, the solution is:
x = 0
y = 100
z = 0

There are no one rupee or five rupee coins in the bag, and there are 100 two rupee coins.

Answer

Given:

A bag contains coins of one rupee, two rupee & five rupees.

The total money in the bag is Rs. 120.

The total number of one rupee and two rupee coins are 35 and in ratio of coins is 2 : 5.

Formula used:
Probability of an event = Favorable ways/Total ways

Calculation:

Number of 1 rupee coins = (2/7 × 35) = 10

Number of 2 rupee coins = (5/7 × 35) = 25

Let the number of 5 rupee coins be x

5x + 1(10) + 2(25) = 120 ⇒ x = 12

Total number of coins = 10 + 25 + 12 = 47

So the bag contain total 47 coins out of which number of five rupee coin is 12

Probability of getting a 5-rupee coin = 12/47

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