**ML Aggarwal CBSE Solutions Class 6 Math 12th Chapter Algebra Exercise 12.3**

**Ex 12.3**

**(1) Form four expressions with numbers 7, 5 and 8 (no variable) using operations of addition, subtraction or multiplication with the condition that every number should be used but not more than once.**

**Solution: **The expressions formed from the given numbers satisfying the given conditions are:

7 x 5 + 8, 5 x 8 – 7, (7 + 5) + 8, 5 x (7 + 8).

In fact, we can form more expressions satisfying the given conditions.

**(2) Which out of the following are expressions with numbers only?**

**(i) 2y + 3**

** (ii) (7 x 20) – 8z**

** (iii) 5 x (21 – 7) + 9 x 2**

** (iv) 5 x 11n**

** (v) (5 x 4) – 45 + p**

**(vi) 3 x (11 + 7) – 24 ÷ 3.**

**Solution: **(iii) 5 x (21 – 7) + 9 x 2 & (vi) 3 x (11 + 7) – 24 ÷ 3 are expressions with numbers only.

**(3) (i) x + 5**

**Solution: **addition; 5 added to x

**(ii) y – 7**

**Solution: **subtraction; 7 subtracted from y

**(iii) 3z**

**Solution: **multiplication; z multiplied by 3

**(iv) p/5**

**Solution: **division, p divided by 5

**(v) 2x + 17**

**Solution: **multiplication and addition, first x multiplied by 2 and then 17 added to the product

**(vi) 3y – 5**

**Solution: **multiplication and subtraction, first y multiplied by 3 and then 5 subtracted from the product.

**(vii) -7m + 2/3**

**Solution: **multiplication and addition, first m multiplied by -7 and then 2/3 added to the product.

**(viii) x/3 – 15**

**Solution: **division and subtraction, first x divided by 3 and then 15 subtracted from the quotient.

**(4) Write expressions for the following:**

**(i) 7 added to p**

**Ans. **p + 7

**(ii) p subtracted from 7**

**Ans. **7 – p

**(iii) p multiplied by 7**

**Ans. **7 x p = 7p

**(iv) p divided by 7**

**Ans. **p / 7

**(v) 7 divided by p**

**Ans. **7 / p

**(vi) 7 subtracted from –m**

**Ans. **–m – 7

**(vii) p multiplied by -5**

**Ans. **-5 x p = -5p

**(viii) –p divided by 5**

**Ans. **–p / 5

**(5) Write expressions:**

**(i) 11 added to 2m**

**Ans. **2m + 11

**(ii) 11 subtracted from 2m**

**Ans. **2m – 11

**(iii) 3 added to 5 times y**

**Ans. **5y + 3

**(iv) 3 subtracted from 5 times y**

**Ans. **5y – 3

**(v) y is multiplied by -8 and then 5 is added to the result**

**Ans. **-8y + 5

**(vi) y is multiplied by 5 and then the result is subtracted from 16**

**Ans. **16 – 5y

**(6) Write the following in mathematical form using signs and symbols**

**(i) 6 more than thrice a number x**

**Solution: **3x + 6

**(ii) 7 taken away from y**

**Solution: **y – 7

**(iii) 3 less than quotient of x by y.**

**Solution: **x/y – 3

**(7) Form six expressions using t and 4 . Use not more than one number operation and every expression must have t in it.**

**Solution: **t + 4. T – 4, 4t, t/4, 4/t, 4 – t

**(8) Form expressions using y, 2 and 7. Use only two different number operations and every expression must have y in it.**

**Solution: **2y + 7, 2y – 7, 7y + 2, 7y – 2, y/2 + 7, y/2 – 7….

**(9) A student scored x marks in English but the teacher deducted 5 marks for bad handwriting. What was the students final score in English?**

**Solution: **students scored x marks

Deducted score for bad handwriting x – 5

Then, Students final score = x – 5

**(10) Raju’s father’s age is 2 years more than 3 times Raju’s age. If Raju’s present age is y years, then what is his father’s age?**

**Solution: **Raju’s present age = y years.

3 time of Raju’s age = 3y

According to the questions, it is said that his father is 2 years more than 3 times of Rajus age.

Then, his father age = 3y + 2

**(11) Mohini is x years old. Express the following in algebraic form:**

**(i) three times Mohini’s age next year**

**(ii) four times Mohini’s age 3 years ago.**

**(iii) the present age of Mohini’s uncle, if his uncle is 5 times as old as Mohini will be two years from now.**

**(iv) the present age of Mohini’s cousin, if her cousin is two years less than one-third of Mohini’s age 5 years ago.**

**Solution: **(i) 3 (x + 1) years

(ii) 4 (x – 3) years.

(iii) 5 (x + 2) years.

(iv) (1/3(x – 5) -2) years

**(12) A cuboidal box has height h cm. Its length is 5 times the height and breadth is 10 cm less than the length. Express the length and the breadth of the box in terms of the height.**

**Solution: **Cuboidal box height – h cm

Questions said, length is 5 times the height. So length is = 5h

Breadth is 10 cm less than the length.

So, the breadth is 5h – 10

**(13) A bus travels at v km per hour. It is going from Delhi to Jaipur. After the bus has travelled 5 hours, Jaipur is still 20 km away. What is the distance from Delhi to Jaipur?**

**Solution: **Bus speed = v km/hr

It has travelled 5 hours. Then distance covered = 5v

Jaipur is still 20 km away, after travelled 5 hours.

∴ Total distance from Delhi to Jaipur = 5v + 20

**(14) Solution:**

(i) The cost of a book is 3 times the cost of a notebook.

(ii) The cost of oil per litre is 5 times the cost of rice per kg.

(iii) The speed of a bus is 10 km per hour more than the speed of a truck.

(iv) Tony puts q marbels on the table. He has 8q marbels in his box.

(v) Our class has n students. The school has 20n students.

(vi) Raju’s uncle is 4 times older than Raju and his aunt is 3 years younger than his uncle.

(vii) The total number of dots is 5 times the number of rows.