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The sum of two numbers is 360. If 65% of one number is equal to 85% of the other. What is the largest number among them?
- a)204
- b)156
- c)256
- d)214
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The sum of two numbers is 360. If 65% of one number is equal to 85% of...
Let the one number be x.
Other number = 360 – x
Now 65% of x = 85% of (360 – x)
⇒ 65 x + 85x = 85 × 360
⇒ 150x = 85 × 360
⇒
Other number = 360 – x
Now 65% of x = 85% of (360 – x)
⇒ 65 x + 85x = 85 × 360
⇒ 150x = 85 × 360
⇒
Most Upvoted Answer
The sum of two numbers is 360. If 65% of one number is equal to 85% of...
Given:
- The sum of two numbers is 360.
- 65% of one number is equal to 85% of the other.
To find:
- The largest number among them.
Let's assume the two numbers are x and y.
So, we have the following equations:
1) x + y = 360 (equation 1)
2) 65% of x = 85% of y (equation 2)
Solving the equations:
- In equation 2, we can rewrite the percentages as decimals:
0.65x = 0.85y
- Dividing both sides by 0.65:
x = (0.85/0.65)y
x = 1.308y
Substituting the value of x in equation 1:
1.308y + y = 360
2.308y = 360
y = 360/2.308
y ≈ 156.25
So, the value of y is approximately 156.25.
Substituting the value of y in equation 1 to find x:
x + 156.25 = 360
x = 360 - 156.25
x ≈ 203.75
So, the value of x is approximately 203.75.
Since we need to find the largest number, the largest number among x and y is 203.75, which is option A: 204.
- The sum of two numbers is 360.
- 65% of one number is equal to 85% of the other.
To find:
- The largest number among them.
Let's assume the two numbers are x and y.
So, we have the following equations:
1) x + y = 360 (equation 1)
2) 65% of x = 85% of y (equation 2)
Solving the equations:
- In equation 2, we can rewrite the percentages as decimals:
0.65x = 0.85y
- Dividing both sides by 0.65:
x = (0.85/0.65)y
x = 1.308y
Substituting the value of x in equation 1:
1.308y + y = 360
2.308y = 360
y = 360/2.308
y ≈ 156.25
So, the value of y is approximately 156.25.
Substituting the value of y in equation 1 to find x:
x + 156.25 = 360
x = 360 - 156.25
x ≈ 203.75
So, the value of x is approximately 203.75.
Since we need to find the largest number, the largest number among x and y is 203.75, which is option A: 204.
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