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Divide 56 into two parts such that three times the first part exceeds one-third of the second by 48. Then the two parts are
- a)(20,36)
- b)(25,31)
- c)(24,32)
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Divide 56 into two parts such that three times the first part exceeds ...
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Divide 56 into two parts such that three times the first part exceeds ...
Given information
- The sum of two parts is 56.
- Three times the first part exceeds one-third of the second by 48.
To find out
- The two parts.
Solution
Let's assume the two parts as x and y, where x is the first part and y is the second part.
From the given information, we can write two equations as follows:
Equation 1: x + y = 56 (The sum of two parts is 56.)
Equation 2: 3x = (1/3)y + 48 (Three times the first part exceeds one-third of the second by 48.)
We need to solve these two equations to find the values of x and y.
Solving Equation 1 for y, we get:
y = 56 - x
Substituting this value of y in Equation 2, we get:
3x = (1/3)(56 - x) + 48
Simplifying the above equation, we get:
9x = 560 - 3x + 144
12x = 704
x = 58.67
But we know that x is the first part, which cannot be a decimal value. Therefore, we need to check the given options to get the two parts.
Checking option A: (20, 36)
The sum of two parts is 20 + 36 = 56, which satisfies Equation 1.
Three times the first part (3*20 = 60) exceeds one-third of the second (36/3 = 12) by 48, which satisfies Equation 2.
Hence, the two parts are (20, 36).
Therefore, the correct answer is option A.
Note: We can also solve Equation 2 for y and substitute the value of y in Equation 1 to get the value of x. But checking the given options is a quicker method.
- The sum of two parts is 56.
- Three times the first part exceeds one-third of the second by 48.
To find out
- The two parts.
Solution
Let's assume the two parts as x and y, where x is the first part and y is the second part.
From the given information, we can write two equations as follows:
Equation 1: x + y = 56 (The sum of two parts is 56.)
Equation 2: 3x = (1/3)y + 48 (Three times the first part exceeds one-third of the second by 48.)
We need to solve these two equations to find the values of x and y.
Solving Equation 1 for y, we get:
y = 56 - x
Substituting this value of y in Equation 2, we get:
3x = (1/3)(56 - x) + 48
Simplifying the above equation, we get:
9x = 560 - 3x + 144
12x = 704
x = 58.67
But we know that x is the first part, which cannot be a decimal value. Therefore, we need to check the given options to get the two parts.
Checking option A: (20, 36)
The sum of two parts is 20 + 36 = 56, which satisfies Equation 1.
Three times the first part (3*20 = 60) exceeds one-third of the second (36/3 = 12) by 48, which satisfies Equation 2.
Hence, the two parts are (20, 36).
Therefore, the correct answer is option A.
Note: We can also solve Equation 2 for y and substitute the value of y in Equation 1 to get the value of x. But checking the given options is a quicker method.
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Divide 56 into two parts such that three times the first part exceeds one-third of the second by 48. Then the two parts area)(20,36)b)(25,31)c)(24,32)d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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