RS Aggarwal 2021-2022 for Class 6 Maths Solutions Chapter 9- Linear Equations in One Variable
RS Aggarwal Class 6 Math Solution Chapter 9- Linear Equations in One Variable Exercise 9C is available here. RS Aggarwal Class 6 Math Solutions are solved by expert teachers in step by step, which help the students to understand easily. RS Aggarwal textbooks are responsible for a strong foundation in Maths. These textbook solutions help students in exams as well as their daily homework routine. The solutions included are easy to understand, and each step in the solution is described to match the students understanding.
Rs Aggarwal Class 6 Math Solution Chapter 9- Linear Equations in One Variable
Test Paper-9
A.1. A man earns Rs. 25 per hour. How much does he earn in x hours?
Solution:
Earning of the man per hour = Rs 25
Earning of the man in x hours = Rs (25 × x)
= Rs 25x
Q2. The cost of 1 pen is Rs. 16 and the cost of 1 pencil is Rs. 5. What is the coast of x pens and y pencils?
Solution:
Cost of 1 pen = Rs 16
∴ Cost of x pens = Rs 16 × x
= Rs 16x
Now, cost of 1 pencil = Rs 5
∴ Cost of y pencils = Rs 5 × y
= Rs 5y
∴ Total cost of x pens and y pencils = Rs (16x + 5y)
Q3. Lalit earns Rs. x per day and spends Rs. y per day. How much does he save in 30 days?
Solution:
Lalit earns per day = Rs x
∴ Lalit earns in 30 days = Rs 30 × x
= Rs 30x
Now, Lalit expense per day = Rs y
∴ Lalit expends in 30 days = Rs 30 × y
= Rs 30y
∴ In 30 days, Lalit saves = (Total earnings − Total expenditure)
= Rs (30x − 30y)
= Rs 30(x − y)
Q4. Three times a number added to 8 gives 20. Find the number.
Solution:
Let the required number be x.
Three times this number is 3x.
According to question,
⇒ 3x + 8 = 20
⇒ 3x = 20 − 8
⇒ 3x = 12
⇒ x = `frac\{cancel 12^4}{cancel 3}`
⇒ x = 4
∴ Required number = 4
Q5. If x = 1, y = 2 and z = 3, find the value of `x^2 + y^2 + 2xyz`.
Solution:
Given:
x =1
y = 2
z = 3
Substituting x = 1, y = 2 and z = 3
`(x^2 + y^2 + 2xyz)`
= `(1)^2 +( 2)^2 + 2(1)(2)(3)`
= 1 + 4 + 12
= 17
Q6. Solve: 4x + 9 = 17.
Solution:
4x + 9 = 17
⇒ 4x = 17 − 9
⇒ 4x = 8
⇒ x = `frac\{cancel 8^2}{cancel 4}`
⇒ x = 2
Q7. Solve: 3(x + 2) − 2(x − 1) = 7
Solution:
3(x + 2) − 2(x − 1) = 7
⇒ 3x + 6 − 2x + 2 = 7
⇒ x = 7 − 6 − 2
⇒ x = 7 − 8
⇒ x = − 1
Q8. Solve: `frac\{2x}{5}` − `frac\{x}{2}` = `frac\{5}{2}`
Solution:
`frac\{2x}{5}` − `frac\{x}{2}` = `frac\{5}{2}`
⇒ `frac\{4x − 5x}{10}` = `frac\{5}{2}`
⇒ `frac\{− x}{10}` = `frac\{5}{2}`
⇒ − x = `frac\{5 × 10}{2}`
⇒ − x = `frac\{cancel 50^25}{cancel 2}`
⇒ x = − 25
Q9. The sum of three consecutive natural number is 51. Find the numbers.
Solution:
Let the three consecutive natural numbers be x, (x + 1) and (x + 2).
∴ x + (x + 1) + (x + 2) = 51
⇒ 3x + 3 = 51
⇒ 3x = 51 − 3
⇒ 3x = 48
⇒ x = `frac\{cancel 48^16}{cancel 3}`
⇒ x = 16
Thus, the three natural numbers are
x = 16, x + 1 = 17 and x + 2 = 18.
Q10. After 16 years, Seema will be three times as old as she is now. Find her present age.
Solution:
Let the present age of Seema be x years.
After 16 years,
Age of Seema = (x + 16) years
According to question,
∴ x + 16 = 3x
⇒ 16 = 3x − x
⇒ 2x = 16
⇒ x = `frac\{cancel 16^8}{cancel 2}`
⇒ x = 8 years
B. Mark (✓) against the correct answer in each of the following:
Q11. By how much does 1 exceed 2x − 3y − 4?
(a) 2x − 3y − 5
(b) 2x − 3y − 3
(c) 5 − 2x + 3y
(d) none of these
Solution: Correct option is (c) 5 − 2x + 3y
∴1 − (2x − 3y − 4)
= 1 − 2x + 3y + 4
= 5 − 2x + 3y
∴ 1 exceeds 2x − 3y − 4 by 5 − 2x + 3y.
Q12. What must be added to `5x^3 − 2x^2 + 6x + 7` to make the sum `x^3 + 3x^2 − x + 1`?
(a) `4x^3 − 5x^2 + 7x + 6`
(b) `− 4x^3 + 5x^2 − 7x − 6`
(c) `4x^3 + 5x^2 − 7x + 6`
(d) none of these
Solution: Correct option is (b) `− 4x^3 + 5x^2 − 7x − 6`
To get required number,
we subtract `(5x^3 − 2x^2 + 6x + 7)` from `(x^3 + 3x^2 − x + 1)`.
`(x^3 + 3x^2 − x + 1)` − `( 5x^3 − 2x^2 + 6x + 7)`
⇒ `x^3 + 3x^2 − x + 1 − 5x^3 + 2x^2 − 6x − 7`
⇒ `x^3 − 5x^3 + 3x^2 + 2x^2− x − 6x + 1 − 7`
⇒ `−4x^3 + 5x^2 − 7x − 6`
Q13. 2x − [3y − {2x − (y − x)}] = ?
(a) 5x − 4y
(b) 4y − 5x
(c) 5y − 4x
(d) 4x − 5y
Solution: Correct option is (a) 5x − 4y
2x − [3y − {2x − (y − x)}]
= 2x − [3y − {2x − y + x}]
= 2x − [3y − {3x − y}]
= 2x − [3y − 3x + y]
= 2x − [4y − 3x]
= 2x − 4y + 3x
= 5x − 4y
Q14. The coefficient of x in − 5xyz is
(a) −5
(b) 5yz
(c) −5yz
(d) yz
Solution: Correct option is (c) −5yz
The coefficient of x in − 5xyz is − 5yz.
Q15. `frac\{1}{3}`(x + y + z) is a
(a) monomial
(b) binomial
(c) trinomial
(d) quadrinomial
Solution: Correct option is (c) trinomial.
It contains three variables, i.e. 'x', 'y' and 'z', So,it is a trinomial
Q16. If `frac\{x}{5}` = 1, then
(a) x = `frac\{1}{5}`
(b) x = 5
(c) x = (5 + 1)
(d) none of these
Solution: Correct option is (b) x = 5
`frac\{x}{5}` = 1
⇒ x = 1 × 5
⇒ x = 5
Q17. If x = 1, y = 2 and z = 3 then `(x^2 + y^2 + z^2)` = ?
(a) 6
(b) 12
(c) 14
(d) 15
Solution: Correct option is (c) 14
`(x^2 + y^2 + z^2)`
= `(1^2 + 2^2 + 3^2)`
= 1 + 4 + 9
= 14
Q18. If `frac\{1}{3}`x + 5 = 8, then x = ?
(a) 3
(b) 6
(c) 9
(d) 12
Solution: Correct option is (c) 9
`frac\{1}{3}`x + 5 = 8
⇒ `frac\{1}{3}`x = 8 −5
⇒ `frac\{1}{3}`x = 3
⇒ x = 3 × 3
⇒ x = 9
C. 19. Fill in the blanks.
(i) An expression having one term is called a ................ .
(ii) An expression having two term is called a ................ .
(iii) An expression having three term is called a ................ .
(iv) 3x − 5 = 7 − x => x = ....... .
(v) `(b^2 − a^2)` − `(a^2 − b^2)` = ........... .
Solution:
(i) monomial
(ii) binomial
(iii) trinomial
(iv) 3x − 5 = 7 − x
⇒, 3x + x = 7 + 5
⇒ 4x = 12
⇒ x = `frac\{cancel 12^3}{cancel 4}`
⇒ x = 3
(v) `b^2 − a^2 − a^2 + b^2`
⇒`2b^2 − 2a^2`
Q20. Write 'T' for true and 'F' for false for each of the statements.
(i) `− 3xy^2z` is a monomial.
(ii) x = `frac\{2}{3}` is solution of 2x + 5 = 8.
(iii) 2x + 3 = 5 is a linear equation.
(iv) The coefficient of x in 5xy is 5.
(v) 8 − x = 5 => x = 3
Solution:
(i) True
(ii) False
2x + 5 = 8
⇒ 2x = 8 − 5
⇒ 2x = 3
⇒ x = `frac\{3}{2}`
not x = `frac\{2}{3}`
(iii) True
This is because the maximum power of the variable x is 1
(iv) False
The coefficient of x in 5xy would be 5y..
(v) True
8 − x = 5
⇒ 8 − 5 = x
⇒ 3 = x
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