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The ratio of two numbers is 3:4 , if 7 is added to both the numbers the ratio becomes 4:15 . find the smaller number?
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The ratio of two numbers is 3:4 , if 7 is added to both the numbers th...
Understanding the Problem:
The problem provides us with two ratios and asks us to find the smaller number in these ratios.
Given Information:
- Initial ratio of two numbers: 3:4
- Ratio after adding 7 to both numbers: 4:15
Let's Solve the Problem Step by Step:
Step 1: Set up the Equations
Let the two numbers be 3x and 4x, as the ratio is 3:4. After adding 7 to both numbers, the new ratio becomes 4:15. Therefore, the new numbers are (3x + 7) and (4x + 7).
Step 2: Set up the Equation based on the Ratios
According to the given information, we can set up the following equations:
(3x + 7) / (4x + 7) = 4 / 15
Step 3: Solve the Equation
Cross multiplying the equation gives:
15(3x + 7) = 4(4x + 7)
45x + 105 = 16x + 28
45x - 16x = 28 - 105
29x = -77
x = -77 / 29
x = -7
Step 4: Find the Smaller Number
Substitute x = -7 back into the equation for the smaller number:
3x = 3(-7) = -21
Answer:
The smaller number is -21.
The problem provides us with two ratios and asks us to find the smaller number in these ratios.
Given Information:
- Initial ratio of two numbers: 3:4
- Ratio after adding 7 to both numbers: 4:15
Let's Solve the Problem Step by Step:
Step 1: Set up the Equations
Let the two numbers be 3x and 4x, as the ratio is 3:4. After adding 7 to both numbers, the new ratio becomes 4:15. Therefore, the new numbers are (3x + 7) and (4x + 7).
Step 2: Set up the Equation based on the Ratios
According to the given information, we can set up the following equations:
(3x + 7) / (4x + 7) = 4 / 15
Step 3: Solve the Equation
Cross multiplying the equation gives:
15(3x + 7) = 4(4x + 7)
45x + 105 = 16x + 28
45x - 16x = 28 - 105
29x = -77
x = -77 / 29
x = -7
Step 4: Find the Smaller Number
Substitute x = -7 back into the equation for the smaller number:
3x = 3(-7) = -21
Answer:
The smaller number is -21.
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The ratio of two numbers is 3:4 , if 7 is added to both the numbers the ratio becomes 4:15 . find the smaller number?
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The ratio of two numbers is 3:4 , if 7 is added to both the numbers the ratio becomes 4:15 . find the smaller number? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The ratio of two numbers is 3:4 , if 7 is added to both the numbers the ratio becomes 4:15 . find the smaller number? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of two numbers is 3:4 , if 7 is added to both the numbers the ratio becomes 4:15 . find the smaller number?.
The ratio of two numbers is 3:4 , if 7 is added to both the numbers the ratio becomes 4:15 . find the smaller number? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The ratio of two numbers is 3:4 , if 7 is added to both the numbers the ratio becomes 4:15 . find the smaller number? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of two numbers is 3:4 , if 7 is added to both the numbers the ratio becomes 4:15 . find the smaller number?.
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