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Bag contains 23 number of coins in the form of 1 rupee, 2 rupee and 5 rupee coins. The total sum of the coins is 43. The ratio between 1 rupee and 2 rupees coins is 3: 2, Then the number of 1 rupee coins.
(a) 12
(b) 8
(c) 10
(d) 16?
(a) 12
(b) 8
(c) 10
(d) 16?
Most Upvoted Answer
Bag contains 23 number of coins in the form of 1 rupee, 2 rupee and 5 ...
To solve the problem of determining the number of 1 rupee coins in a bag containing 1 rupee, 2 rupee, and 5 rupee coins, we can use a systematic approach.
Given Information
- Total number of coins = 23
- Total value of coins = 43 rupees
- Ratio of 1 rupee coins to 2 rupee coins = 3:2
Let’s Define Variables
- Let the number of 1 rupee coins = 3x
- Let the number of 2 rupee coins = 2x
- Let the number of 5 rupee coins = y
Setting Up Equations
1. From the total number of coins:
Equation 1:
\[
3x + 2x + y = 23 \quad \Rightarrow \quad 5x + y = 23
\]
2. From the total value of coins:
Equation 2:
\[
1(3x) + 2(2x) + 5y = 43 \quad \Rightarrow \quad 3x + 4x + 5y = 43 \quad \Rightarrow \quad 7x + 5y = 43
\]
Solve the Equations
Now we have a system of equations:
1. \(5x + y = 23\)
2. \(7x + 5y = 43\)
From Equation 1, express y:
\[
y = 23 - 5x
\]
Substituting y into Equation 2:
\[
7x + 5(23 - 5x) = 43
\]
\[
7x + 115 - 25x = 43
\]
\[
-18x = -72 \quad \Rightarrow \quad x = 4
\]
Calculate the Number of Coins
Substituting x back:
- Number of 1 rupee coins = \(3x = 12\)
- Number of 2 rupee coins = \(2x = 8\)
- Number of 5 rupee coins:
\[
y = 23 - 5(4) = 3
\]
Final Answer
Thus, the number of 1 rupee coins is **12**.
The correct option is **(a) 12**.
Given Information
- Total number of coins = 23
- Total value of coins = 43 rupees
- Ratio of 1 rupee coins to 2 rupee coins = 3:2
Let’s Define Variables
- Let the number of 1 rupee coins = 3x
- Let the number of 2 rupee coins = 2x
- Let the number of 5 rupee coins = y
Setting Up Equations
1. From the total number of coins:
Equation 1:
\[
3x + 2x + y = 23 \quad \Rightarrow \quad 5x + y = 23
\]
2. From the total value of coins:
Equation 2:
\[
1(3x) + 2(2x) + 5y = 43 \quad \Rightarrow \quad 3x + 4x + 5y = 43 \quad \Rightarrow \quad 7x + 5y = 43
\]
Solve the Equations
Now we have a system of equations:
1. \(5x + y = 23\)
2. \(7x + 5y = 43\)
From Equation 1, express y:
\[
y = 23 - 5x
\]
Substituting y into Equation 2:
\[
7x + 5(23 - 5x) = 43
\]
\[
7x + 115 - 25x = 43
\]
\[
-18x = -72 \quad \Rightarrow \quad x = 4
\]
Calculate the Number of Coins
Substituting x back:
- Number of 1 rupee coins = \(3x = 12\)
- Number of 2 rupee coins = \(2x = 8\)
- Number of 5 rupee coins:
\[
y = 23 - 5(4) = 3
\]
Final Answer
Thus, the number of 1 rupee coins is **12**.
The correct option is **(a) 12**.
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Bag contains 23 number of coins in the form of 1 rupee, 2 rupee and 5 rupee coins. The total sum of the coins is 43. The ratio between 1 rupee and 2 rupees coins is 3: 2, Then the number of 1 rupee coins.(a) 12(b) 8(c) 10(d) 16?
Question Description
Bag contains 23 number of coins in the form of 1 rupee, 2 rupee and 5 rupee coins. The total sum of the coins is 43. The ratio between 1 rupee and 2 rupees coins is 3: 2, Then the number of 1 rupee coins.(a) 12(b) 8(c) 10(d) 16? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Bag contains 23 number of coins in the form of 1 rupee, 2 rupee and 5 rupee coins. The total sum of the coins is 43. The ratio between 1 rupee and 2 rupees coins is 3: 2, Then the number of 1 rupee coins.(a) 12(b) 8(c) 10(d) 16? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Bag contains 23 number of coins in the form of 1 rupee, 2 rupee and 5 rupee coins. The total sum of the coins is 43. The ratio between 1 rupee and 2 rupees coins is 3: 2, Then the number of 1 rupee coins.(a) 12(b) 8(c) 10(d) 16?.
Bag contains 23 number of coins in the form of 1 rupee, 2 rupee and 5 rupee coins. The total sum of the coins is 43. The ratio between 1 rupee and 2 rupees coins is 3: 2, Then the number of 1 rupee coins.(a) 12(b) 8(c) 10(d) 16? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Bag contains 23 number of coins in the form of 1 rupee, 2 rupee and 5 rupee coins. The total sum of the coins is 43. The ratio between 1 rupee and 2 rupees coins is 3: 2, Then the number of 1 rupee coins.(a) 12(b) 8(c) 10(d) 16? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Bag contains 23 number of coins in the form of 1 rupee, 2 rupee and 5 rupee coins. The total sum of the coins is 43. The ratio between 1 rupee and 2 rupees coins is 3: 2, Then the number of 1 rupee coins.(a) 12(b) 8(c) 10(d) 16?.
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