## RD Sharma Solutions Class 6 Chapter 8 Exercise 8.1

**Exercise 8.1**

**Question 1: Write the following using numbers, literals and signs of basic operations. State what each letter represents: **

**(i) The diameter of a circle is twice its radius.**

**(ii) The area of a rectangle is the product of its length and breadth. **

**(iii) The selling price equals the sum of the cost price and profit.**

**(iv) The total amount equals the sum of the principal and the interest.**

**(v) The perimeter of a rectange is two times the sum of its length and breadth.**

**(vi) The perimeter of a square is four times its side.**

**Solution:**

(i) Let r and d be the radius and diameter of the circle, respectively.

Therefore, d = 2r

(ii) Let l and b be the length and breadth of the rectangle. respectively.

Therefore, area of rectangle = lb

(iii) Let s, c and p be the selling price, cost price and profit, respectively.

Therefore, s = c + p

(iv) Let T, p and i be the total amount, principal and interest, respectively.

Therefore, T = p + i

(v) Let land b be the length and breadth of the rectangle, respectively.

Therefore, perimeter of rectangle = 2(l + b)

(vi) Let a be the side of the square.

Therefore, permiter of the square = 4a

**Question 2: Write the following using numbers, literals and signs of basic operations:**

** (i) The sum of 6 and x.**

**(ii) 3 more than a number y.**

** (iii) One- third of a number x.**

** (iv) One- half of the sum of number x and y.**

** (v) Number y less than a number 7.**

** (vi) 7 taken away from x.**

** (vii) 2 less than the quotient of x by y**

** (viii) 4 times x taken away from one-thirs of y.**

** (ix) Quotient of x by 3 is multiplies by y.**

**Answer:**

(i) The sum of 6 and x is 6 + x.

(ii) 3 more than a number y means y + 3.

(iii) One-third of a number x is \(\frac{x}{3}\)

(iv) One-half of the sum of numbers x and y is \(\frac{\left (x + y \right )}{2}\)

(v) Number y less than a number 7 means 7 – y.

(vi) 7 taken away from x means x – 7.

(vii) 2 less than the quotient of x by y is \(\frac{x}{y} – 2\)

(viii) 4 times x taken away from one-third of y is \(\frac{y}{3} – 4x\)

(ix) Quotient of x by 3 is multiplied by y means: \(\frac{ x y }{ 3 }\)

**Question 3: Think of a number. Multiply it by 5. Add 5 to the result. Subtract y from this result. What is the result?**

**Answer:**

Let the number be x.

On multiplying the number by 5. we get: 5x

Further, adding 6 to 5x. we get: 5x + 6

Finally, on subtracting y from 5x + 6,

we get: 5x + 6 â€“ y

**Question 4: The number of rooms on the ground floor of a building is 12 less than the twice of the numbers of rooms on the first floor. If the first floor has x rooms, how many rooms does the ground floor has?**

**Answer: **

Let the number of rooms on the ground floor be y.

It is given that the number of rooms on the first floor is x; therefore, we have:

y =2 X x – 12

= 2x – 12

Thus, the number of rooms on the ground floor is 2x – 12.

**Question 5: Binny spends Rs. A daily and saves Rs. B per week. What is her income for 2 weeks?**

**Answer:**

It is given that Binny spends Rs. a in one day.

Money spent by him in one week = 7 X a = 7a

It is further given that he saves Rs. b in one week; therefor we have:

Total income in one week = Total expenditure in one week + Total saving in one week

= 7a + b

Therefore, Binny’s total income in 2 weeks = 2 X (7a + b)

= Rs. (14a + 2b)

**Question 6: Rahul score 80 marks in English and x marks in Hindi. What is his total scores in the two subjects?**

**Answer:**

Marks obtained in English = 80

Marks obtained in Hindi = x

Total marks obtained = 80 + x

**Question 7: Rohit covers x centimeters in one step. How much distance does he covers in y steps?**

**Answer:**

It is given that Rohit covers x cm in one step.

Therefore, distance covered by him in y steps = x X y = x y cm

**Question 8: One apple weighs 75 grams and one orange weighs 40 grams. Determine the weigh of x apples an y oranges.**

**Answer:**

Weight of an apple = 75 grams

Wright of an orange = 40 grams

Weight of x apples = 75 X x = 75x grams

Weight of y oranges = 40 X y = 40y grams

Total weight of x apples and y oranges = (75x + 40y) grams

**Question 9: One pencil costs Rs. 2 and one fountain pen costs Rs. 15. What is the cost of x pernicls and y fountain pens?**

**Answer:**

Cost of one pencil = Rs. 2

Cost of x pencils = Rs. 2x

Cost of one fountain pen = Rs. 15

Cost of y fountain pens = Rs. 15y

Total cost of x pencils and y fountain pens = Rs. (2x + 15y)