Page 8.13 of RD Sharma Solutions for Class 6 Maths Chapter 8 - Introduction to Algebra, showing objective type questions and solutions.

You've uploaded a page from RD Sharma Solutions for Class 6 Maths, Chapter 8 – Introduction to Algebra, specifically Page 8.13, which contains Objective Type Questions. The task is to mark the correct alternative for each question and explain the solution.

Let’s go through each question one by one with clear explanations:

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Question 1:

> 5 more than twice a number x is written as

Options:
(a) 5 + x + 2
(b) 2x + 5
(c) 2x − 5
(d) 5x + 2

✔ Correct Answer: (b) 2x + 5

Explanation:
- “Twice a number x” means 2 × x = 2x
- “5 more than” means we add 5 to that.
- So, 2x + 5

Option (a) adds 5, x, and 2 — incorrect grouping.
Option (c) subtracts 5 — wrong operation.
Option (d) multiplies x by 5 — misinterprets “twice”.

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Question 2:

> The quotient of x by 2 is added to 5 is written as

Options:
(a) x/2 + 5
(b) 2/x + 5
(c) (x+2)/5
(d) x/(2+5)

✔ Correct Answer: (a) x/2 + 5

Explanation:
- “Quotient of x by 2” means x ÷ 2 = x/2
- “Added to 5” means + 5
- So, x/2 + 5

Option (b) is reciprocal — 2 divided by x — wrong.
Option (c) adds 2 to x then divides by 5 — not what’s asked.
Option (d) divides x by 7 — incorrect grouping.

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Question 3:

> The quotient of x by 3 is multiplied by y is written as

Options:
(a) x/3y
(b) 3x/y
(c) 3y/x
(d) xy/3

✔ Correct Answer: (d) xy/3

Explanation:
- “Quotient of x by 3” = x/3
- “Multiplied by y” = × y
- So, (x/3) × y = (x × y)/3 = xy/3

Option (a) x/3y could be misinterpreted as x/(3y), which is different.
In algebra, xy/3 clearly means (x × y) ÷ 3.
Options (b) and (c) reverse the operations or variables.

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Question 4:

> 9 taken away from the sum of x and y is

Options:
(a) x + y − 9
(b) 9 − (x+y)
(c) x+y/9
(d) 9/x+y

✔ Correct Answer: (a) x + y − 9

Explanation:
- “Sum of x and y” = x + y
- “9 taken away from” means subtract 9 → so (x + y) − 9

Option (b) does the reverse: 9 minus the sum — wrong order.
Option (c) only divides y by 9 — misinterprets “taken away”.
Option (d) is meaningless in this context.

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Question 5:

> The quotient of x by y added to the product of x and y is written as

Options:
(a) x/y + xy
(b) y/x + xy
(c) xy + x/y
(d) xy + y/x

✔ Correct Answer: (a) x/y + xy

Explanation:
- “Quotient of x by y” = x ÷ y = x/y
- “Product of x and y” = x × y = xy
- “Added to” means we add them: x/y + xy

Note: Addition is commutative, so xy + x/y (option c) is mathematically equivalent.
But since option (a) matches the exact wording (“quotient... added to product”), and is listed first, it’s the best choice.

However, both (a) and (c) are algebraically equal. But in multiple-choice questions like this, they often expect the expression in the order mentioned.

✔ So, (a) x/y + xy is the intended correct answer.

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## ✔ Final Answers Summary:

| Question | Correct Option |
|----------|----------------|
| 1 | (b) 2x + 5 |
| 2 | (a) x/2 + 5 |
| 3 | (d) xy/3 |
| 4 | (a) x + y − 9 |
| 5 | (a) x/y + xy |

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## 📌 Key Concepts Used:
- Twice a number → multiply by 2
- Quotient → division
- Sum → addition
- Product → multiplication
- Taken away → subtraction
- Order of operations and proper grouping matter!

These problems test your ability to translate English phrases into algebraic expressions, which is foundational in algebra.

Let me know if you’d like to practice similar problems! 😊