### Mathematics Class 10 Lab Manual | 21 Lab Activities

Mathematics Lab Manual Class X   lab activities for class 10 with complete observation Tables strictly according to the CBSE syllabus also very useful & helpful for the students and teachers.

# Linear Equations in One Variable

Important extra questions on Linear Equations in One Variable class VIII strictly according to the DAV board and CBSE Board, necessary for board examinations.

# Math Assignment Linear Equations

Question 1.
Solve the following and verify the result     $\frac{x+2}{x+5}=\frac{x}{x+6}$

Ans. x = - 4

Question 2.
Solve the following and verify the result      $\frac{y-1}{3}-\frac{y-2}{4}=1$
Ans. y = 1

Question 3.
Solve the following and verify the result     $\frac{1}{4}y+\frac{1}{6}y=y-7$
Ans.  y = 12

Question 4.
Solve and verify the result   $\frac{2-7x}{1-5x}=\frac{3+7x}{4+5x}$
Ans. x = 1/2

Question 5.
Solve and verify the result      $\frac{6x+7}{3x+2}=\frac{4x+13}{2x+5}$
Ans. x = 3

Question 6.
(i)  Solve and verify the result    $\frac{6x+1}{3}+1=\frac{x-3}{6}$
Ans.   x = -1

(ii) Solve the following :  $\large \frac{\frac{3}{5}x-3}{\frac{1}{3}x-1}=\frac{6}{5}$
Ans. x = 9

Question 7.
(i)  Solve for x:    $\frac{1}{x}+\frac{1}{x}+\frac{1}{x}=3$
Ans.  x = 1

Question 8. Solve the following equation

$\frac{x^{2}-(x+2)(x+3)}{6x+1}=\frac{2}{3}$
Ans.  x = - 20/27

Question 9.  Solve the following equation

$\frac{17(2-x)-5(x+12)}{1-7x}=8$
Ans. x = 1

Question 10.
Solve the following equation

$\frac{2(3y-4)+6}{3y-(4+5y)}=\frac{3}{5}$

Question 11.
Solve the following equation

$\frac{y^{2}-(y+2)(y-2)}{y+2}=\frac{1}{2}$

Question 12.
Solve the following equation
$\frac{(x+1)(4x-3)-4x^{2}+5}{4x+1}=\frac{1}{3}$
Question 13.
Three numbers are in the ratio 2 : 3 : 5. Find the numbers, if the sum of their squares is 608.
Ans. Required Numbers are: 8, 12, 20 and  x = 4

Question 14.
Three consecutive whole numbers are such that if they are divided by 5, 3, 4 respectively, the sum of the quotients is 40. Find the numbers.
Ans. Three consecutive whole numbers are: 50, 51, 52

Question 15.
I have a total of Rs 300 as coins of denomination of 1, 2 and 5. The number of 2 rupee coins is 3 times the number of 5 rupee coins. The total number of coins are 160. How many coins of each denomination are with me ?
Ans. Total Rs 1 coins = 80, Total Rs 2 coins = 60, Total Rs 5 coins = 20,

Question 16.
The sum of two positive integers is 120. The integers are in the ratio 2 : 3. Find the integers.
Ans. Required Numbers are : 48, 72  and  x = 24

Question 17.
The sum of the digits of a two digit number is 10. The number obtained by interchanging the digits exceeds the original number by 36. Find the original number.
Ans. Unit digit = 7, Tens digit = 3, Required Number = 37

Question 18.
One fifth of a number increased by 5 is equal to 4 less than one fourth of that number. Find the number.
Ans. Required No. = 180

Question 19.
Priya's father decided to distribute apples among patients of a hospital on her birthday. He brought 963 apples to distribute to the patients. The male patients are three more than two times female patients and children are two times female patients in hospital. Each patient will get only one apple. How many apples female patients will get?
Ans. Number of female patients in the school = 192

Question 20.
A money box contains one rupee and 2 rupee coins in ratio 3 : 5. If the total value of coins in the money box is Rs. 78, find the number of one rupee coins.
Ans. Number of Rs 1 coin = 18, Number of Rs 2 coin = 30.

Question 21.
A number consists of two digits whose sum is 8. If 18 is added to the number, its digits are reversed. Find the number.
Ans. Required No. = 35

Question 22.
The numerator of a fraction is 4 less than the denominator. If 1 is added to both its numerator and denominator, it becomes 1⁄2. Find the fraction.
Ans. Required Fraction is = 3/7

Question 23.
Arvind has a piggy bank. It is full of one rupee and fifty paise coins. It contains 3 times as many fifty paise coins as one rupee coins. The total amount of the money in the piggy bank is ₹ 35. How many coins of each kind are there in the piggy bank?
Ans. Total Rs 1 coins = 14, Total 50 Paise coins = 42

Question 24.
Kumar is 3 years older than Anita. Six years ago, Kumar's age was 4 times Anita's age. Find the present ages of Kumar and Anita.
Ans. Age of Anita = 18 Years, Age of Kumar = 54 Years

Question 25.
Arnav's father is 49 years old. He is nine years older than four times Arnav's age. set up an equation to find arnav's age and find Arnav's age.
Ans. 4x + 9 = 49 ⇒  x = 10
Arnav's age = 10 years

Question 26
Present ages of Sehaj and Saloni are in ratio 5 : 4. Eight years from now, the ratio of their ages will be 6 : 5. Find their present ages.
Ans. Age of Sehaj = 40 Years,  Age of Saloni = 32 Years.

Question 27
The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2 . Find the rational number.
Ans. Required Fraction = 13/21

Question 28
A steamer goes down stream from one part to another in 9 hrs. It covers the same distance up steam in 10 hrs. If the speed of the stream is 1 km/hr. Find the speed of the steamer in still water.
Ans. Speed of steamer in still water = 19 km/h

Question 29
Two years ago, Dilip was three times as old as his son and two years hence, twice his age will be equal to five times that of his son. Find their present ages.

Ans. ATQ 2(3x + 4) = 5(x + 4)
⇒ x = 12
Father's Present age = x + 2 = 12 + 2 = 14 Years
Son's Present age = x + 2 = 3 ✕12 + 2 = 38 Years

Question 30
Reena went shopping and spent half of what she had on buying fruits. Out of the money she was left with, she gave ₹ 5 to a beggar. She spent one-third of the remaining money on rickshaw fare. When she reached home, she found that she has exactly ₹ 100 left. How much money she initially had?

Ans. Money she initally have = Rs. 320
Sol. Hint: Let total money she initially have = x
ATQ   $\frac{1}{2}x+5+\frac{1}{3}\left(\frac{1}{2}x-5\right)+100=x$
Solving this equation we get x = Rs. 320

Question 31.
A boat covers a certain distance downstream in one and a half hours. It covers the same distance upstream in 2 hours. The speed of the boat in still water is 35 km/hr. Find the speed of stream.
Ans. Speed of the stream = 5 km/h

Question 32.
The digits of a two digit number differ by 3. If the digits are interchanged and the resulting number is added to the original number, we get 143. What can be the original number?
Ans. Original Number  Either 58 or 85

Question 33.
A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers become twice the other new number. What are the numbers?

Ans. One number = 35,
Another number = 7
Solution Hint. Let numbers are x and y
ATQ  x = 5y
Again ATQ,  x + 21 = 2(y + 21)
Putting y = 5y we get
y = 7 and  x = 35

Question 34.
Ram is cashier in a bank. He has currency notes of denominations of Rs100, ₹ 50 and ₹ 10 in the ratio 2 : 3 : 5. The total cash with him is ₹1,00,000. How many notes of each denominations does he have?

Ans. No. of Rs 100 notes = 500
No. of Rs 50 notes = 750
No. of Rs 10 notes = 1250

Question 35
A steamer goes upstream from one port to another in 6 hours. It covers the same distance downstream in 5 hours. If the speed of the stream is 2 km/hr, find the speed of the steamer in still water.
Ans. x = 22 km/h

Question 36
A purse has only ten rupees and fifty rupees notes in it. The number of ten rupees notes is one third of the number of fifty rupees notes. If the purse has a total of ₹800, find the number of ten rupees notes.
Ans. No. Rs 50 notes = 15
No. of Rs 10 notes = 5

Question 37

Solve the following  $\sqrt{1+\frac{49}{576}}=1+\frac{x}{24}$
Ans. x = 1