10th Maths - Book Back Answers - Chapter 3 Exercise 3.6 - English Medium Guides

  

 

SSLC / 10th - Maths - Book Back Answers - Chapter 3 Exercise 3.6 - English Medium

Tamil Nadu Board 10th Standard Maths - Chapter 3 Exercise 3.6: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 3 Exercise 3.6 – Maths from the Tamil Nadu State Board 10th Standard textbook. These detailed answers have been carefully prepared by our expert teachers at KalviTips.com.

    We have explained each answer in a simple, easy-to-understand format, highlighting important points step by step under the relevant subtopics. Students are advised to read and memorize these subtopics thoroughly. Once you understand the main concepts, you’ll be able to connect other related points with real-life examples and confidently present them in your tests and exams.

    By going through this material, you’ll gain a strong understanding of Chapter 3 Exercise 3.6 along with the corresponding book back questions and answers (PDF format).

Question Types Covered:

• 1 Mark Questions: Choose the correct answer, Fill in the blanks, Identify the correct statement, Match the following 
• 2 Mark Questions: Answer briefly 
• 3, 4, and 5 Mark Questions: Answer in detail

All answers are presented in a clear and student-friendly manner, focusing on key points to help you score full marks.

All the best, Class 10 students! Prepare well and aim for top scores. Thank you!

Chapter 3 Algebra Ex 3.6

1. Simplify
(i) $\frac{x(x+1)}{x-2}=\frac{x(x-1)}{x-2}$
Answer Key:
$\frac{x(x+1)}{x-2}=\frac{x(x-1)}{x-2}=\frac{x(x+1)+x(x-1)}{x-2}$

$=\frac{{\mathrm{x}}^2+\mathrm{x}+{\mathrm{x}}^2-\mathrm{x}}{\mathrm{x}-2}=\frac{2\mathrm{x}}{\mathrm{x}-2}$ 

 

(ii) $\frac{x+2}{x+3}+\frac{x-1}{x-2}$
Answer Key:
$\frac{x+2}{x+3}+\frac{x-1}{x-2}=\frac{(x+2)(x-2)-(x-1)(x+3)}{(x+3)(x-2)}$

 

(iii) $\frac{x^3}{x-y}+\frac{y^3}{y-x}=\frac{x^3}{x-y}+\frac{y^3}{-1(x-y)}$
Answer Key:
$=\frac{x^3}{x-y}-\frac{y^3}{x-y}$
$=\frac{x^3-y^3}{x-y}$(using a³ – b³ = (a – b) (a² + ab + b²))
$=\frac{(\mathrm{x}-\mathrm{y})({\mathrm{x}}^2+\mathrm{xy}+{\mathrm{y}}^2)}{\mathrm{x}-\mathrm{y}}$
= x² + xy + y²

 

2. Simplify
(i)$\frac{(2\mathrm{x}+1)(\mathrm{x}-2)}{\mathrm{x}-4}-\frac{(2{\mathrm{x}}^2-5\mathrm{x}+2)}{\mathrm{x}-4}$
Answer Key:

(ii) $\frac{4\mathrm{x}}{{\mathrm{x}}^2-1}-\frac{\mathrm{x}+1}{\mathrm{x}-1}$
Answer Key:

 

3. Subtract $\frac{1}{{\mathrm{x}}^2+2}$ from $\frac{2{\mathrm{x}}^3+{\mathrm{x}}^2+3}{({\mathrm{x}}^2+2{)}^2}$
Answer Key:

4. Which rational expression should be subtracted from $\frac{{\mathrm{x}}^2+6\mathrm{x}+8}{{\mathrm{x}}^3+8}$
Answer Key:

 

5. If A = $\frac{2\mathrm{x}+1}{2\mathrm{x}-1}$, B = $\frac{2\mathrm{x}-1}{2\mathrm{x}+1}$ find $\frac{1}{\mathrm{A}-\mathrm{B}}-\frac{2\mathrm{B}}{{\mathrm{A}}^2-{\mathrm{B}}^2}$
Answer Key:

 

6. If A =$\frac{\mathrm{x}}{\mathrm{x}+1}$ B = $\frac{1}{\mathrm{x}+1}$ prove that $\frac{(\mathrm{A}+\mathrm{B}{)}^2+(\mathrm{A}-\mathrm{B}{)}^2}{\mathrm{A}+\mathrm{B}}-\frac{2({\mathrm{x}}^2+1)}{\mathrm{x}(\mathrm{x}+1{)}^2}$
Answer Key:

 

7. Pari needs 4 hours to complete a work. His friend Yuvan needs 6 hours to complete the same work. How long will it take to complete if they work together?
Answer Key:
Pari: time required to complete the work = 4 hrs.
∴ In 1 hr. he will complete = $\frac{1}{4}$ of the work.
= $\frac{1}{4}$w.
Yuvan: Time required to complete the work = 6 hrs.
∴ In 1 hr. he will complete the $\frac{1}{6}$of the work
= $\frac{1}{6}$w
Working together, in 1 hr. they will complete $\frac{\mathrm{w}}{4}+\frac{\mathrm{w}}{6}$ of the work.
=$\frac{6\mathrm{w}+4\mathrm{w}}{24}=\frac{5}{12}\mathrm{w}$
∴ To complete the total work time taken
= $\frac{\mathrm{w}}{\frac{5}{12}\mathrm{w}}=\frac{12}{5}$=125 = 2.4 hrs. [∵ (4) hrs = 4 × 60 = 24 min]
= 2 hrs 24 minutes.

 

8. Iniya bought 50 kg of fruits consisting of apples and bananas. She paid twice as much per kg for the apple as she did for the banana. If Iniya bought ? 1800 worth of apples and ₹ 600 worth bananas, then how many kgs of each fruit did she buy?

Answer Key:
 Let the weight of applies be a kg.
Let the weight of bananas be b kg.
a + b = 50
ax = ₹ 1800 ………….. (1)
by = ₹ 600 ………… (2)
x = 2y …………… (3)
Use (3) in (1) ⇒ a(2y) = 1800
y = $\frac{900}{\mathrm{a}}$ ………….. (4)
Use (4) in (2) ⇒ b$\frac{900}{\mathrm{a}}$ = 600
∵ 3b = 2a …………….. (5)
∵ a + b = 50
a + $\frac{2\mathrm{a}}{3}$ = 50 ⇒ $\frac{5\mathrm{a}}{3}$ = 50
⇒ a = 50 × $\frac{3}{5}$
= 30
∴ b = 20
∴ Iniya bought 30 kg of applies and 20 kg of bananas
= 30
.’. b = 20.
.’. Iniya bought 30 kg of applies and 20 kg of bananas.