# Word Problems for Linear equations with Solutions

Given below are the Class 10 Maths Word problems for Linear equations in Two Variables with answers. These are important questions for the examination
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Linear Equations word Problems formulas

Question 1
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 of apples left with you”. B replies, “if you give me 10 of your apples, I will the same number of apples as left with you.” Find the number of apples with P andQ separately

Hint:
$x +10 =2(y-10)$
$x-10 = y + 10$
Answer (70, 50)

Question 2
On selling a T. V. at 5% gain and a fridge at 10% gain,Reliance digital gains Rs 2000. But if its 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.

Hint:
$\frac {5}{100} x + \frac {10}{100} y =2000$
$\frac {10}{100} x - \frac {5}{100} y = 1500$
Answer (20,000, 10,000)

Question 3
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.

Hint:
$x - y =2$
$2x - \frac {y}{2} = 40$
x=26 and y=24

Question 4
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.

Hint:
$(x+5)=3 (y+5)$
$(x-5) =7(y-5)$
Answer 40 year, 10 year

Question 5
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.

Hint:
Case -1
$x - y =3$
$2x - \frac {y}{2} = 30$
(19,16)
Case -2
$y - x =3$
$2x - \frac {y}{2} = 30$
( 21,24)

Question 6
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.

Hint:
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

Question 7
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.

Hint:
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

Question 8
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 minutes. Find the speed of the boat in still water and also speed of the stream.

Hint:
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

Question 9
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.

Hint:
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

Question 10
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.

Hint:
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

Question 11
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.

Hint:
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

Question 12
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

Question 13
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?

Hint:
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

Question 14
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?

Hint:
Let x and y be the amount invested
Then
$.12x + .1 y=130$
$.12y + .1x= 134$
Solving
x=500 ,y=700

Question 15
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.

Hint:

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

Question 16
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.

Hint:
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

Question 17
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.

Hint:
Let x and y be the actual price of tea-set and the soup-set
then
.15y -.5 x=7
.5x + .1 y=13
Solving these ,we get
x=100 any y=80
Question 18
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?

Hint:
Let x be the time taken by man and y be the time taken by boy
Then
$\frac {4}{x} + \frac {6}{y}= \frac {1}{20}$
$\frac {3}{x} + \frac {4}{y}= \frac {1}{28}$
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

Question 19
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.

Question 20
A two- digit number is obtained by either multiplying the sum of the digits by 8 and then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3. Find the number.

Hint:
Let the two digit number is 10x+y
Then
$8 \times (x+y) -5= 10x +y$
$16 \times (x-y) + 3= 10x +y$
Solving the above , we get x=8 ,y=3 Hence Number is 83

Question 21
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.

Hint:
Let Rana has x and y bananas in lot A and B
Then
$\frac {2x}{3} +y= 400$
$x + \frac {4y}{5}= 460$
Solving the above , we get x=300 ,y=200 Hence total bananas are 500

Question 22
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?
Question 23
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

Question 24
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

Question 25
The sum of two digit number and the number obtained by reversing the order of its digit is 99. If the digits differ by 3, find the number.

Answer x=6

Question 26
The sum of a numerator and denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduces to 1/3. Find the fraction.

Answer 5/3

Question 27
The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.

Answer 4/7

Question 28
A is elder to B by 2 years. A’s father F is twice as old as A and B is twice as old as his sister S. If the ages of the father and sister differ by 40 years, find the age of A.

Answer 20 years

Question 29
Ten years ago, a father was twelve times as old as his son and ten years hence, he will be twice as old as his son will be then. Find their present ages.

34 years, 12 years

Question 30
The ratio of incomes of two persons is 11 : 7 and the ratio of their expenditures is 9 : 5. If each of them manages to save Rs. 400 per month, find their monthly incomes.

Answer 1400, 2200
Question 31
A villager went to a hotel in a town with his big family. They consumed 23 idlies, 18 pooris, 7 dosas and 19 vadas. The bill came to Rs. 108. On the next day, they consumed 34 idlies, 8 vadas, 22 pooris and 7 dosas. The bill came to Rs. 114. If one idli costs the same as a vada, what is the cost of one poori?

Hint:
Let p for Poorie, i for Idli, v for Vada, d for Dosa.
Then
23i + 18p + 7d + 19v = 108
34i+ 8v+ 22p + 7d = 114
Now One idli costs same as vada.
So, i = v
So both the above equation becomes
23v + 18p + 7d + 19v = 108 or c 108
34v+ 8v+ 22p + 7d = 114 or 42v+ 22p+ 7d = 114
Subtract these
42v+ 22p+ 7d - (42v+ 22p+ 7d) = 114 - 108
4p = 6
p = Rs 1.50

## Summary

This Class 10 Maths Word Problems Worksheet for Linear equations in Two Variables with answers is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail.

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### Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20