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The ratio of the ages of Mr. Rajendra and Rahul is 7:2. After 8 years their ages will be in the ratio 8:3. Find their present ages? Ch - 8, Ratio and Proportion?
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The ratio of the ages of Mr. Rajendra and Rahul is 7:2. After 8 years ...
Given:
The ratio of the ages of Mr. Rajendra and Rahul is 7:2.
After 8 years, their ages will be in the ratio 8:3.
To find:
Their present ages.
Assumption:
Let the present age of Mr. Rajendra be 7x and the present age of Rahul be 2x.
Solution:
Step 1: Set up equations
The ratio of their ages is given as 7:2, so we can set up the equation:
7x / 2x = 7/2
After 8 years, their ages will be in the ratio 8:3, so we can set up the equation:
(7x + 8) / (2x + 8) = 8/3
Step 2: Solve the equations
Solving the first equation:
7x / 2x = 7/2
Cross-multiplying, we get:
7 * 2x = 2 * 7x
14x = 14x
Since the equation is true for all non-zero values of x, we can conclude that the first equation is satisfied.
Solving the second equation:
(7x + 8) / (2x + 8) = 8/3
Cross-multiplying, we get:
3(7x + 8) = 8(2x + 8)
21x + 24 = 16x + 64
21x - 16x = 64 - 24
5x = 40
x = 40 / 5
x = 8
Step 3: Calculate their present ages
Substituting the value of x in 7x and 2x:
Present age of Mr. Rajendra = 7x = 7 * 8 = 56 years
Present age of Rahul = 2x = 2 * 8 = 16 years
Answer:
The present age of Mr. Rajendra is 56 years and the present age of Rahul is 16 years.
The ratio of the ages of Mr. Rajendra and Rahul is 7:2.
After 8 years, their ages will be in the ratio 8:3.
To find:
Their present ages.
Assumption:
Let the present age of Mr. Rajendra be 7x and the present age of Rahul be 2x.
Solution:
Step 1: Set up equations
The ratio of their ages is given as 7:2, so we can set up the equation:
7x / 2x = 7/2
After 8 years, their ages will be in the ratio 8:3, so we can set up the equation:
(7x + 8) / (2x + 8) = 8/3
Step 2: Solve the equations
Solving the first equation:
7x / 2x = 7/2
Cross-multiplying, we get:
7 * 2x = 2 * 7x
14x = 14x
Since the equation is true for all non-zero values of x, we can conclude that the first equation is satisfied.
Solving the second equation:
(7x + 8) / (2x + 8) = 8/3
Cross-multiplying, we get:
3(7x + 8) = 8(2x + 8)
21x + 24 = 16x + 64
21x - 16x = 64 - 24
5x = 40
x = 40 / 5
x = 8
Step 3: Calculate their present ages
Substituting the value of x in 7x and 2x:
Present age of Mr. Rajendra = 7x = 7 * 8 = 56 years
Present age of Rahul = 2x = 2 * 8 = 16 years
Answer:
The present age of Mr. Rajendra is 56 years and the present age of Rahul is 16 years.
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The ratio of the ages of Mr. Rajendra and Rahul is 7:2. After 8 years their ages will be in the ratio 8:3. Find their present ages? Ch - 8, Ratio and Proportion?
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The ratio of the ages of Mr. Rajendra and Rahul is 7:2. After 8 years their ages will be in the ratio 8:3. Find their present ages? Ch - 8, Ratio and Proportion? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about The ratio of the ages of Mr. Rajendra and Rahul is 7:2. After 8 years their ages will be in the ratio 8:3. Find their present ages? Ch - 8, Ratio and Proportion? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of the ages of Mr. Rajendra and Rahul is 7:2. After 8 years their ages will be in the ratio 8:3. Find their present ages? Ch - 8, Ratio and Proportion?.
The ratio of the ages of Mr. Rajendra and Rahul is 7:2. After 8 years their ages will be in the ratio 8:3. Find their present ages? Ch - 8, Ratio and Proportion? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about The ratio of the ages of Mr. Rajendra and Rahul is 7:2. After 8 years their ages will be in the ratio 8:3. Find their present ages? Ch - 8, Ratio and Proportion? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of the ages of Mr. Rajendra and Rahul is 7:2. After 8 years their ages will be in the ratio 8:3. Find their present ages? Ch - 8, Ratio and Proportion?.
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