1)karan is 3 times older to teja now. After 5 year their ages will be in the ratio 11:10.Find their present ages?
2)the distance between two towns on a national highway is 760 km. A and B start simultaneously from these cities on their bikes towards each other. They meet after 4 hrs and if the speed of B is 10kmph more than that of A. Find their speeds?
Answers
here is your answer
The first question needs some corrections
Q.[1]
Given data :-
- Karan is 3 times older to Teja
- After 5 year their ages will be in the ratio 11:10
Solution :-
Let, age of Teja be x
→ age of Teja = x years ..... ( 1 )
Hence, according to given
→ age of Karan = 3x years ..... ( 2 )
According to given after 5 years
→ age of Karan : age of Teja
= 3x + 5 : x + 5 ..... ( 3 )
According to given ratio of their ages after 5 year
→ age of Karan : age of Teja
= 11:10 ..... ( 4 )
Now, from ( 3 ) & ( 4 )
→ 3x + 5 : x + 5 = 11 : 10
We can write it as
→ {3x + 5}/{x+5} = 11/10
→ 10 {3x + 5} = 11 {x + 5}
→ 30x + 50 = 11x + 55
→ 30x - 11x = 55 - 50
→ 19x = 5
→ x = 5/19
→ age of Teja = x years
→ age of Teja = 5/19 years
Put value of x in eq. ( 2 )
→ age of Karan = 3x years
→ age of Karan = 3 × 5/19 years
→ age of Karan = 15/19 years
Put value of x in eq. ( 3 )
→ age of Karan : age of Teja
= 3x + 5 : x + 5
→ age of Karan : age of Teja
= 3 × 5/19 + 5 : 5/19 + 5
→ age of Karan : age of Teja
= 15/19 + 5 : 100/19
→ age of Karan : age of Teja
= 110/19 : 100/19
Hence, before 5 year age of Karan and age of Teja is 15/19 and 5/19 respectively. and after five year age of Karan and age of Teja is 110/19 and 100/19 respectively.
Q.[2]
Given data :-
- The distance between two towns on a national highway is 760 km.
- A and B start simultaneously from these cities on their bikes towards each other.
- They meet after 4 hrs and if the speed of B is 10kmph more than that of A.
Solution :-
Let, speed of A be ' x '
→ Speed of A = x
Hence, according to given
→ Speed of B = x + 10 .....( 1 )
→ Total time taken by A and B = 4 hour
→ Total distance travel by A and B = 760km
Now, we use formula of relative speed
→ Relative speed of A and B
= {Total speed}/{Total time}
→ x + x + 10 = 760/4
→ 2x + 10 = 190
→ 2x = 190 - 10
→ 2x = 180
→ x = 180/2
→ x = 90 km/hr
Hence, speed of A is 90 km/hr.
Put value of x in eq. ( 1 )
→ Speed of B = x + 10
→ Speed of B = 90 + 10
→ Speed of B = 100 km/hr
Hence, speed of B is 100 km/hr.
Hence, speed of A and B is 90 km/hr and 100 km/hr respectively.