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Two numbers are in ratio of 4 ∶ 5 respectively. If each number is reduced by 25, then the ratio becomes 3 ∶ 4. Find the largest number.
- a)100
- b)125
- c)130
- d)135
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Two numbers are in ratio of 4 ∶ 5 respectively. If each number is redu...
Given Data:
Let the two numbers be 4x and 5x respectively.
First Condition:
According to the first condition,
4x - 25 = 3y and 5x - 25 = 4y
where x and y are the new reduced numbers.
Solving the Equations:
From the above equations, we can solve for x and y:
4x - 25 = 3y
4x - 25 = 4(5x - 25)/5
4x - 25 = 4x - 100/5
4x - 25 = 4x - 20
-25 = -20
This leads to a contradiction, which means the first condition is invalid.
Second Condition:
Let's consider the second condition and solve for x and y:
4x - 25 = 5y and 5x - 25 = 4y
4x - 25 = 5y
4x - 25 = 5(4x - 25)/4
4x - 25 = 5x - 125/4
4x - 25 = 5x - 31.25
-25 = -31.25
This condition is also invalid.
Correct Approach:
Let's solve the problem using the correct approach:
4x/5 - 25 = 3y and 5x/5 - 25 = 4y
4x/5 - 25 = 3y
4x - 125 = 15y
4x = 15y + 125
5x/5 - 25 = 4y
x - 25 = 4y
x = 4y + 25
Substitute x = 4y + 25 into 4x = 15y + 125:
4(4y + 25) = 15y + 125
16y + 100 = 15y + 125
16y - 15y = 125 - 100
y = 25
Now, find the largest number:
5x = 5(25)
5x = 125
x = 125
Therefore, the largest number is 125. So, option B is correct.
Let the two numbers be 4x and 5x respectively.
First Condition:
According to the first condition,
4x - 25 = 3y and 5x - 25 = 4y
where x and y are the new reduced numbers.
Solving the Equations:
From the above equations, we can solve for x and y:
4x - 25 = 3y
4x - 25 = 4(5x - 25)/5
4x - 25 = 4x - 100/5
4x - 25 = 4x - 20
-25 = -20
This leads to a contradiction, which means the first condition is invalid.
Second Condition:
Let's consider the second condition and solve for x and y:
4x - 25 = 5y and 5x - 25 = 4y
4x - 25 = 5y
4x - 25 = 5(4x - 25)/4
4x - 25 = 5x - 125/4
4x - 25 = 5x - 31.25
-25 = -31.25
This condition is also invalid.
Correct Approach:
Let's solve the problem using the correct approach:
4x/5 - 25 = 3y and 5x/5 - 25 = 4y
4x/5 - 25 = 3y
4x - 125 = 15y
4x = 15y + 125
5x/5 - 25 = 4y
x - 25 = 4y
x = 4y + 25
Substitute x = 4y + 25 into 4x = 15y + 125:
4(4y + 25) = 15y + 125
16y + 100 = 15y + 125
16y - 15y = 125 - 100
y = 25
Now, find the largest number:
5x = 5(25)
5x = 125
x = 125
Therefore, the largest number is 125. So, option B is correct.
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Community Answer
Two numbers are in ratio of 4 ∶ 5 respectively. If each number is redu...
Given:
Original ratio of two numbers = 4 : 5
Modified ratio of two numbers = 3 : 4
Each number when reduced by 25
Calculation:
Let the original numbers be 4x and 5x.
According to the question,
⇒ 16x - 100 = 15x - 75
⇒ 16x - 15x = 100 - 75
⇒
x = 25Larger number = 5x = 5 × 25 = 125
∴ The largest number is 125.
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Two numbers are in ratio of 4 ∶ 5 respectively. If each number is reduced by 25, then the ratio becomes 3 ∶ 4. Find the largest number.a)100b)125c)130d)135Correct answer is option 'B'. Can you explain this answer?
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