- What is Linear equations
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- Linear equations Solutions
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- Graphical Representation of Linear equation in one and two variable
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- Steps to Draw the Given line on Cartesian plane
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- Simultaneous pair of Linear equation
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- Algebraic Solution of system of Linear equation
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- Simultaneous pair of Linear equation in Three Variable
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- Steps to solve the Linear equations

- NCERT Solutions Exercise 3.1
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- NCERT Solutions Exercise 3.2
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- NCERT Solutions Exercise 3.3,3.4,3.5
- NCERT Solutions Exercise 3.6
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- NCERT Solutions Exercise 3.7

- Problem and Solutions
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- Linear equations Problems
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- Linear equation worksheet
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- Linear equation word problems
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- Linear equations graphical problems

P and Q each have certain number of apples. A says to B, “if you give me 10 of your apples, I will have twice the number ofapples left with you”. B replies, “if you give me 10 of your apples, I will the same number ofapples as left with you.” Find the number ofapples with P andQ separately

$x +10 =2(y-10)$

$x-10 = y + 10$

Answer (70, 50)

On selling a T. V. at 5% gain and a fridge at 10% gain,Reliance digitalgains Rs 2000. But ifits sells the T. V. at 10% gain and the fridge at 5% loss. He gains Rs 1500 on the transaction. Find the actual prices of T. V. and fridge.

$ \frac {5}{100} x + \frac {10}{100} y =2000$

$\frac {10}{100} x - \frac {5}{100} y = 1500$

Answer (20,000, 10,000)

A and B are friends and their ages differ by 2 years. A's father D is twice as old as A and B is twice as old as his sister C. The age of D and C differ by 40 years. Find the ages of A and B.

$x - y =2$

$2x - \frac {y}{2} = 40$

x=26 and y=24

Five years hence, father's age will be three times the age of his son. Five years ago, father was seven times as old as his son. Find their present ages.

$(x+5)=3 (y+5)$

$(x-5) =7(y-5)$

Answer 40 year, 10 year

The ages of two friends Manjit and Ranjit differ by 3 years. Manjit's father Dharam is twice as old as Manjit and Ranjit as twice as old as his sister Jaspreet. The ages of Jaspreet and Dharam differ by 30 years. Find the ages of Manjit and Ranjit.

Case -1

$x - y =3$

$2x - \frac {y}{2} = 30$

(19,16)

Case -2

$y - x =3$

$2x - \frac {y}{2} = 30$

( 21,24)

A takes 3 hours more than B to walk 30 km. But if A doubles his pace, he is ahead of B by one and half hrs. Find their speed of walking.

Let x and y be the speed of A and B

$\frac {30}{x} - \frac {30}{y} = 3$

$\frac {30}{y} - {30}{2x} = \frac {3}{2}$

Now Substituting p=1/x and q=1/y,then solving

p=3/10 and q=1/5

So x=3.3 km/hr and y=5 km/hr

The boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of stream and that of the boat in still water.

Let speed of boat in still water be x km/h and speed of stream be y km/h.

Speed upstream= (x - y) km/h

Speed downstream= (x + y) km/h

$\frac {30}{x-y}+ \frac {44}{x+y} = 10$

$\frac {40}{x-y}+ \frac {55}{x+y} = 13$

Now Substituting $p=\frac {1}{x-y}$ and $q=\frac {1}{x+y}$,then solving

p=1/5 and q=1/11

Hence $x-y=5$ and $x+y =11$, Solving these,

x=8 km/hr and y=3km/hr

A boat goes 24 km upstream and 28 km downstream in 6 hrs. It goes 30 km upstream and 21 km downstream in 6 hrs and 30 min. Find the speed of the boat in still water and also speed of the stream.

This question is exactly same as above question Let speed of boat in still water be x km/h and speed of stream be y km/h.

Speed upstream= (x - y) km/h

Speed downstream= (x + y) km/h

$\frac {24}{x-y}+ \frac {28}{x+y} = 6$

$\frac {30}{x-y}+ \frac {21}{x+y} = 6.5$

Now Substituting $p=\frac {1}{x-y}$ and $q=\frac {1}{x+y}$,then solving

p=1/6 and q=1/14

Hence $x-y=6$ and $x+y =14$, Solving these,

x=10 km/hr and y=4km/hr

A man walks a certain distance with certain speed. If he walks 1/2 km an hour faster, he takes 1 hour less. But, if he walks 1 km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking.

Let v = the rate the man walked, t=time taken originally and d=distance

$d=vt$

Case 1 (faster)

Speed= (v+.5)

time=(t-1) = time taken at the faster speed

Now $distance = velocity \times time$

$vt= (v+.5)(t-1)$

$v - .5t = -.5$ (1)

Case 2 (slower)

speed=(v-1)

time=(t+3)

Now $distance = velocity \times time$

$vt = (v-1)(t+3)$

$-3v + t = -3$ (2)

Solving (1) and (2)

v=4 km/hr ,t=9 hr, hence d= 36 km

Anuj travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes. But, if the travels 200 km by train and the rest by car, he takes half an hour longer. Find the speed of the train and that of the car.

Let x and y be the speed of train and car,then using time= distance/speed

$\frac {400}{x} + \frac {200}{y} = 6.5$

$ \frac {200 }{ x} + \frac {400}{y} = 7$

Now Substituting $p=\frac {1}{x}$ and $q=\frac {1}{y}$,then solving

$400p + 200q=6.5$

$200p +400 q=5$

p=1/100 and q=1/80

hence x=100 km/hr and y=80km/hr

A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream.

This question is exactly same as above question Let speed of boat in still water be x km/h and speed of stream be y km/h.

Speed upstream= (x - y) km/h

Speed downstream= (x + y) km/h

$\frac {12}{x-y}+ \frac {40}{x+y} = 8$

$\frac {16}{x-y}+ \frac {32}{x+y} = 8$

Now Substituting $p=\frac {1}{x-y}$ and $q=\frac {1}{x+y}$,then solving

$12p + 40q=8$

$16p+ 32q=8$

p=1/4 and q=1/8

Hence $x-y=4$ and $x+y =8$, Solving these,

x=6 km/hr and y=2km/hr

Hadi 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.

Similar Question

x=100 km/hr and y=80km/hr

Places X and Y are 100 km apart on a highway. One car starts from X and another from Y 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?

Let x and y be the speed of the cars

Case A( same direction)

Relative speed between the car= (x-y)

Now

$speed= \frac {distance}{time}$

Then $(x-y) = \frac {100}{5} =20$ -(1)

Case B(towards each other)

Relative speed between the car= (x+y)

Now

$speed= \frac {distance}{time}$

Then $(x+y) = \frac {100}{1} =100$ -(2)

Solving (1) and (2)

x=60 km/hr and y=40 km/hr

A person invested some amount at the rate of 12% simple interest and some other amount at the rate of 10% simple interest. He received yearly interest of Rs. 130. But if he had interchanged the amounts invested, he would have received Rs 4 more as interest. How much amount did he invest at different rates?

Let x and y be the amount invested

Then

$.12x + .1 y=130$

$.12y + .1x= 134$

Solving

x=500 ,y=700

Students of a class are made to stand in rows. If one student is extra in a row, there would be 2 rows less. If one student is less in a row there would be 3 rows more. Find the number of students in the class.

Let number of rows is x and number of students is y in a row.

Then total number of students = xy

$ (x-2)(y+1)=xy$ or $x-2y=2$

$(x+3)(y-1)=xy$ or $-x+3y=3$

Solving

x=12 ,y=5

So students are = 12 *5=60

8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days. Find the time taken by one man alone and that by one boy alone to finish the work.

Let x be the time taken by man and y be the time taken by boy

Then

$\frac {8}{x} + \frac {12}{y}= \frac {1}{10}$

$\frac {6}{x} + \frac {8}{y}= \frac {1}{14}$

Substituting p=1/x and q=1/y and solving

p=1/140 and q=1/280

Hence x=140 days and y=280 days

On selling a tea-set at 5% loss and a soup-set at 15% gain, a crockery seller gains Rs. 7. If he sells the tea-sets at 5% gain and the soup-sets at 10% gain, he gains Rs 13. Find the actual price of the tea-set and the soup-set.

4 men and 6 boys can do a piece of work in 20 days. It is done by 3 men and 4 boys in 28 boys. How long would it take for one man or one boy to do it?

After covering a distance of 30 km with a uniform speed there is some defect in a Express train engine and, therefore, its speed is reduced to 4/5 of its original speed. Consequently, the train reaches its destination late by 45 minutes. Had it happened after covering 18 km more, the train would have reached 9 minutes earlier. Find the speed of the train and the distance of journey.

A two- digit number is obtained by either multiplying the sum of the digits by 8 or then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.

Answer 83

Rana had some bananas and he divided them into two lots A and B. He sold first lot at the rate of Rs 2 for 3 bananas and the second lot at the rate of Re. 1 per banana and got a total of Rs 400. If he had sold the first lot at the rate of Rs. 1 per banana and the second lot at the rate of Rs. 4 for 5 bananas, his total collection would have been Rs. 460. Find the total number of bananas he had.

2 men and 7 boys can do a piece of work in 4 days. The same work is done in 3 days by 4 men and 4 boys. How long would it take one man and one boy to do it?

Father's age is three times the sum of his two children's age. After 5 years his age will be twice the sum of the ages of two children. Find the age of father.

Answer 45 years

A chemist has one solution which is 50% acid and a second solution which is 25% acid. How much of each should be mixed to make 10 litres of a 40% acid solution?

Answer 6 and 4 litres

A wizard having powers of mystic incantations and magical medicines seeing a cock, fight going on, spoke privately to both the owners of the cocks. To one he said, "If your bird wins, then you give me your stake money, but if you do not win, I shall give you two- thirds of that." Going to the other, he promised in the same way to give three fourths. From both of them his gain would be only 12 Gold pieces. State money of each of the cock- owners.

Answer 42,40

Given below are the links of some of the reference books for class 10 math.

- Oswaal CBSE Question Bank Class 10 Hindi B, English Communication Science, Social Science & Maths (Set of 5 Books)
- Mathematics for Class 10 by R D Sharma
- Pearson IIT Foundation Maths Class 10
- Secondary School Mathematics for Class 10
- Xam Idea Complete Course Mathematics Class 10

You can use above books for extra knowledge and practicing different questions.

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