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A, B and C play cricket. The ratio of the runs scored by A and B is 3 : 2. The ratio of the runs scored by B and C is 3 : 2. Together, they score 342 runs. How many runs did A make?
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A, B and C play cricket. The ratio of the runs scored by A and B is 3...
Given:
A, B, and C play cricket.
The ratio of the runs scored by A and B is 3:2.
The ratio of the runs scored by B and C is 3:2.
Together, they score 342 runs.
To Find:
How many runs did A make?
Solution:
Let's assume that the runs scored by A, B, and C are 3x, 2x, and 2y, respectively.
Step 1: Analyzing the Ratios
The ratio of the runs scored by A and B is given as 3:2.
So, we can write the equation as:
3x/2x = 3/2
Simplifying the equation, we get:
3x * 2 = 2x * 3
6x = 6x
This equation is satisfied for any value of x.
Similarly, the ratio of the runs scored by B and C is given as 3:2.
So, we can write the equation as:
2x/2y = 3/2
Simplifying the equation, we get:
2x * 2 = 2y * 3
4x = 6y
Step 2: Expressing the Ratios in Terms of x
From the equation 4x = 6y, we can express y in terms of x:
y = 4x/6
y = 2x/3
Substituting this value of y in the equation 2x/2y = 3/2, we get:
2x/(2x/3) = 3/2
2x * (3/2x) = 3/2
6/2 = 3/2
This equation is also satisfied for any value of x.
Step 3: Finding the Value of x
We know that the sum of their runs is 342.
So, we can write the equation as:
3x + 2x + 2y = 342
Substituting the value of y as 2x/3, we get:
3x + 2x + 2(2x/3) = 342
3x + 2x + 4x/3 = 342
9x/3 + 6x/3 + 4x/3 = 342
(9x + 6x + 4x)/3 = 342
19x/3 = 342
Multiplying both sides of the equation by 3, we get:
19x = 342 * 3
19x = 1026
Dividing both sides of the equation by 19, we get:
x = 1026/19
x = 54
Step 4: Finding the Runs Scored by A
We need to find the runs scored by A, which is 3x:
Runs scored by A = 3 * 54 = 162
Answer:
A made 162 runs.
A, B, and C play cricket.
The ratio of the runs scored by A and B is 3:2.
The ratio of the runs scored by B and C is 3:2.
Together, they score 342 runs.
To Find:
How many runs did A make?
Solution:
Let's assume that the runs scored by A, B, and C are 3x, 2x, and 2y, respectively.
Step 1: Analyzing the Ratios
The ratio of the runs scored by A and B is given as 3:2.
So, we can write the equation as:
3x/2x = 3/2
Simplifying the equation, we get:
3x * 2 = 2x * 3
6x = 6x
This equation is satisfied for any value of x.
Similarly, the ratio of the runs scored by B and C is given as 3:2.
So, we can write the equation as:
2x/2y = 3/2
Simplifying the equation, we get:
2x * 2 = 2y * 3
4x = 6y
Step 2: Expressing the Ratios in Terms of x
From the equation 4x = 6y, we can express y in terms of x:
y = 4x/6
y = 2x/3
Substituting this value of y in the equation 2x/2y = 3/2, we get:
2x/(2x/3) = 3/2
2x * (3/2x) = 3/2
6/2 = 3/2
This equation is also satisfied for any value of x.
Step 3: Finding the Value of x
We know that the sum of their runs is 342.
So, we can write the equation as:
3x + 2x + 2y = 342
Substituting the value of y as 2x/3, we get:
3x + 2x + 2(2x/3) = 342
3x + 2x + 4x/3 = 342
9x/3 + 6x/3 + 4x/3 = 342
(9x + 6x + 4x)/3 = 342
19x/3 = 342
Multiplying both sides of the equation by 3, we get:
19x = 342 * 3
19x = 1026
Dividing both sides of the equation by 19, we get:
x = 1026/19
x = 54
Step 4: Finding the Runs Scored by A
We need to find the runs scored by A, which is 3x:
Runs scored by A = 3 * 54 = 162
Answer:
A made 162 runs.
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A, B and C play cricket. The ratio of the runs scored by A and B is 3 : 2. The ratio of the runs scored by B and C is 3 : 2. Together, they score 342 runs. How many runs did A make? Related: Ratio Proportion Variation Practice Questions?
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