Answer :
To solve this problem, we need to look at both parts separately.
Question 26: Age Ratio
Eleven years ago, the ages of Prakash and Shravan were in the ratio 7:10. Let's assume their ages 11 years ago were [tex]7x[/tex] and [tex]10x[/tex] respectively.
Now, we'll find their current ages:
- Prakash's current age = [tex]7x + 11[/tex]
- Shravan's current age = [tex]10x + 11[/tex]
Eight years from now, their ages will be:
- Prakash's age = [tex]7x + 19[/tex]
- Shravan's age = [tex]10x + 19[/tex]
We need to find which given options cannot be the age ratio 8 years from now.
Let's analyze each option:
[tex]11:13[/tex]
[tex]\frac{7x+19}{10x+19} = \frac{11}{13}[/tex]
Solving this equation for [tex]x[/tex] will give potential valid solutions, so let's check other options.
[tex]4:9[/tex]
[tex]\frac{7x+19}{10x+19} = \frac{4}{9}[/tex]
Simplifying and solving the equation shows inconsistencies or complex numbers, which are not valid in this context.
Thus, option B, [tex]4:9[/tex], cannot be the ratio of their ages 8 years from now.
Question 27: Cycling Speed and Distance
Let [tex]d[/tex] be the distance to the destination and [tex]s[/tex] be the original speed of the cyclist.
First condition: If the speed increases by 5 km/hr, it takes 2 hours less:
[tex]\frac{d}{s} - \frac{d}{s+5} = 2[/tex]
Second condition: If the speed decreases by 3 km/hr, it takes 2 hours more:
[tex]\frac{d}{s-3} - \frac{d}{s} = 2[/tex]
These two conditions together form a system of equations and can be solved simultaneously.
Solving these, we typically find the distance [tex]d[/tex].
Through elimination or substitution methods, solve to find [tex]d = 120[/tex].
Therefore, the correct answer to the distance question is option (B) 120 km.
