Abdul travelled 300 km by train and 200 km by taxi, it took him 5 hours 30 minutes . But if 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.

Let the speed of the train be x km / hr that of the taxi be y km / hr . We have the following cases: Case I: When Abdul travels 300 km by train and 200 km by taxi. Time taken by Abdul to travel 300 km by train = 300 x hrs Time taken by Abdul to travel 200 km by taxi = 200 y hrs Total time taken by Abdul to cover 500 km = 300 x + 200 y It is given that total time taken in 5 hours 30 minutes . ⇒ 300 x + 200 y = 5 hours 30 minutes ⇒ 100 3 x + 2 y = 5 30 60 ⇒ 100 3 x + 2 y = 5 1 2 ⇒ 100 3 x + 2 y = 5 11 2 ⇒ 3 x + 2 y = 11 2 × 1 100 ⇒ 3 x + 2 y = 11 200 … i Case II: When Abdul travels 260 km by train and the 240 km by taxi. Time taken by Abdul to travel 260 km by train = 260 x hrs Time taken by Abdul to travel 240 km by taxi = 240 y hrs In this case total time of the journey is 5 hours 36 minutes . ⇒ 260 x + 240 y = 5 hours 36 minutes ⇒ 260 x + 240 y = 5 36 60 ⇒ 260 x + 240 y = 5 6 10 ⇒ 260 x + 240 y = 5 3 5 ⇒ 20 13 x + 12 y = 28 5 ⇒ 13 x + 12 y = 28 5 × 1 20 ⇒ 13 x + 12 y = 7 25 … ( i i ) Putting 1 x = u and 1 y = v , the equations ( i ) and ( i i ) reduces to 3 u + 2 v = 11 200 . . i i i 13 u + 12 v = 7 25 … ( i v ) Multiplying equation ( i i i ) by 6 , the above system of equation becomes 18 u + 12 v = 33 100 … ( v ) Subtracting equation i v from ( v ) we get: 18 u + 12 v = 33 100 ⇒ - 13 u - 12 v = - 7 25 5 u = 33 100 - 7 25 ⇒ 5 u = 33 100 - 7 × 4 25 × 4 ⇒ 5 u = 33 100 - 28 100 ⇒ 5 u = 33 - 28 100 ⇒ u = 5 100 × 1 5 ⇒ u = 1 100 Putting u = 1 100 in equation ( i i i ), we get: 3 u + 2 v = 11 200 ⇒ 3 × 1 100 + 2 v = 11 200 ⇒ 3 100 + 2 v = 11 200 ⇒ 2 v = 11 200 - 3 100 ⇒ 2 v = 11 200 - 3 × 2 100 × 2 ⇒ 2 v = 11 - 6 200 ⇒ 2 v = 5 200 ⇒ v = 1 40 × 1 2 ⇒ v = 1 80 Now, u = 1 100 ⇒ 1 x = 1 100 ⇒ x = 100 and v = 1 80 ⇒ 1 y = 1 80 ⇒ y = 80 Hence, the speed of the train is 100 km / hr and the speed of the taxi is 80 km / hr .

HARD

10th CBSE

IMPORTANT

Earn 100

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.

Important Questions on Pair of Linear Equations in Two Variables

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.10>Q 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 upstream.

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.10>Q 14

Abdul travelled

300 km

by train and

200 km

by taxi, it took him

5 hours 30 minutes

. But if he travels

2 x + 2 y = 20

by train and

240 km

by taxi, he takes

6 minutes

longer. Find the speed of the train and that of the taxi.

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.10>Q 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.

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.10>Q 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.

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.10>Q 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.

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.10>Q 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

1 \frac{1}{2} hours

. Find the speeds of

A

and

B

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.11>Q 1

If in a rectangle, the length is increased and breadth reduced each by

2 units,

the area is reduced by

28

square units. If, however the length is reduced by

1

unit

and the breadth increased by

2 units

, the area increases by

33

square units. Find the area of the rectangle.

HARD

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 3 - Pair of Linear Equations in Two Variables>EXERCISE 3.11>Q 2

The area of a rectangle remains the same if the length is increased by

7

meters

and the breadth is decreased by

3

meters

. The area remains unaffected if the length is decreased by

7

meters

and breadth in increased by

5

meters

. Find the dimensions of the rectangle.

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.

Important Questions on Pair of Linear Equations in Two Variables

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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.