RD Chapter 3 Pair of Linear Equations in Two Variables Ex 3.10 Solutions
Question - 11 : - Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.
Answer - 11 : -
Total distance = 300 km
Let the speed of train = x km/hr
and speed of bus = y km/hr
In first case,
Distance travelled by train = 60 km
and distance by bus = 300 – 60 = 240
and total time taken = 4 hrs
Question - 12 : - Ritu can row downstream 20 km in 2 hours and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.
Answer - 12 : -
Let the speed of rowing in still water = x km/hr
and speed of current of water = y km/hr
Speed of downstream = (x + y) km/hr
and speed of upstream = (x – y) km/hr
Speed of rowing = 6 km/hr and speed of current = 4 km/hr
Question - 13 : - A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream. [NCERT Exemplar]
Answer - 13 : -
Let the speed of the motorboat in still water and the speed of the stream are u km/h and v km/h, respectively.
Then, a motorboat speed in downstream = (u + v) km/h
and a motorboat speed in upstream = (u – v) km/h
Motorboat has taken time to travel 30 km upstream,
Question - 14 : - Abdul travelled 300 km by train and 200 km by taxi, it took him 5 hours 30 minutes. But it he travels 260 km by train and 240 km by taxi he takes 6 minutes longer. Find the speed of the train and that of the taxi. (CBSE 2006C)
Answer - 14 : -
Let the speed of train = x km/hr
and speed of taxi = y km/hr
In first case,
Question - 15 : - A train covered a certain distance at a uniform speed. If the train could have been 10 km/hr. faster, it would have taken 2 hours less than the Scheduled time. And, if the train were slower by 10 km/ hr ; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
Answer - 15 : -
Let the speed of the train = x km/hr
and time taken = y hours
Distance = speed x time = x x y = xy km
In the first case,
Speed = (x + 10) km/hr
Time = (y – 2) hours
Distance = (x + 10) (y – 2) = xy
=> xy – 2x+ 10y – 20 = xy
=> -2x + 10y – 20 = 0
=> x – 5y + 10 = 0 ……….(i)
In second case,
Speed of the train = (x – 10) km/hr
and time = (y + 3) hours
Distance = (x – 10) (y + 3) = xy
=> xy + 3x – 10y – 30 = xy
=> 3x – 10y – 30 = 0 ………(ii)
Multiplying (i) by 2 and (ii) by 1
Question - 16 : - Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of two cars ?
Answer - 16 : -
Distance between A and B places = 100 km
Let the speed of first car (starting from A) = x km/hr
and speed of second car (starting from B) = y km/hr
In first case, when the cars travel in the same direction
Time when they meet = 5 hours
Distance travelled by first car in 5 hours = 5x km
and by second car = 5y = 5y km
5x – 5y = 100
=> x – y = 20 …(i)
In second case, when the cars travel in the opposite direction
Time when they meet = 1 hour
Distance travelled by first case = x x 1 = x km
and by second car = y x 1 = y km
x + y = 100 ……..(i)
Adding (i) and (ii)
2x = 120 => x = 60
Subtracting (i) from (ii)
2y = 80 => y = 40
Speed of first car = 60 km/hr and speed of second car = 40 km/hr
Question - 17 : - While covering a distance of 30 km. Ajeet takes 2 hours more than Amit. If Ajeet doubles his speed, he would take 1 hour less than Amit. Find their speeds of walking.
Answer - 17 : -
Total distance = 30 km
Let speed of Ajeet = x km/hr
and speed of Amit = y km/hr
Now according to the condition,
Speed of Ajeet = 5 km/hr and speed of Amit = 7.5 km/hr
Question - 18 : - A takes 3 hours more than B to walk a distance of 30 km. But if A doubles his pace (speed) he is ahead of B by 1
hours. Find their speeds.
Answer - 18 : -
Let speed of A = x km/hr
and speed of B = y km/hr
Total distance in first case,