The present ages of Ramu and Ravi are in the ratio of 4:3. After 5 years the ratio of their ages will be 5:4. Find their present ages, respectively.
- A15 years,20 years
- B15 years,12 years
- C10 years,15 years
- D20 years,15 years
Solution & Step-by-step Explanation
Let the present ages of Ramu and Ravi be 4x and 3x respectively.
After 5 years:
Age of Ramu=4x+5
Age of Ravi=3x+5
According to the question, the new ratio is 5:4:
3x+5
4x+5
=
4
5
Cross-multiplying to solve for x:
4(4x+5)=5(3x+5)
16x+20=15x+25
16x−15x=25−20
x=5
Now, substitute x=5 into their present ages:
Present age of Ramu=4×5=20 years
Present age of Ravi=3×5=15 years
After 5 years:
Age of Ramu=4x+5
Age of Ravi=3x+5
According to the question, the new ratio is 5:4:
3x+5
4x+5
=
4
5
Cross-multiplying to solve for x:
4(4x+5)=5(3x+5)
16x+20=15x+25
16x−15x=25−20
x=5
Now, substitute x=5 into their present ages:
Present age of Ramu=4×5=20 years
Present age of Ravi=3×5=15 years