ML Aggarwal CBSE Solutions Class 6 Math Twelveth Chapter Algebra Exercise 12.3

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.


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