### Linear Equations in One Variable - Solutions 4

CBSE Class –VIII Mathematics

NCERT Solutions

CHAPTER - 2

Linear Equations in One Variable (Ex. 2.4)

NCERT Solutions

CHAPTER - 2

Linear Equations in One Variable (Ex. 2.4)

1. Amina thinks of a number and subtracts from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?

Ans. Let Amina thinks of a number

According to the question,

Hence, the number is 4.

2. A positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?

Ans. Let another number be

Then positive number =

According to the question,

Hence, another number = 7

and positive number = =35

3. Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?

Ans. Let the unit place digit of a two-digit number be

Therefore, the tens place digit =

2-digit number = 10 x tens place digit + unit place digit

Original number =

According to the question, New number

= Original number + 27

10x + 9 - x = 90 - 10x +x +27

Hence, the 2-digit number =

= 10 (9 – 6) + 6

=

= 30 + 6 = 36

4. One of the two digits of a two-digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?

Ans. Let the unit place digit of a two-digit number be

Therefore, the tens place digit =

2-digit number = 10 x tens place digit + unit place digit

Original number = =

According to the question, New number + Original number = 88

5. Shobo’s mother’s present age is six times Shobo’s present age. Shobo’s age five years from now will be one third of his mother’s present age. What are their present ages?

Ans. Let Shobo’s present age be years.

And Shobo’s mother’s present age = years

According to the question,

years.

Hence, Shobo’s present age = 5 years

And Shobo’s mother’s present age = = 30 years.

6. There is a narrow rectangular plot, reserved for a school, in Mahuli village. The length and breadth of the plot are in the ratio 11 : 4. At the rate Rs. 100 per meter it will cost the village panchayat Rs. 75,000 to fence the plot. What are the dimensions of the plot?

Ans. Let the length and breadth of the rectangular plot be and respectively.

Perimeter of the plot = = = 750 m

We know that Perimeter of rectangle = 2 (length + breadth)

Therefore, according to the question,

Hence, length of rectangular plot = = 275 m

And breadth of rectangular plot = = 100 m

7. Hasan buys two kinds of cloth materials for school uniforms, shirt material that costs him Rs. 50 per metre and trouser material that costs him Rs. 90 per metre. For every 2 metres of the trouser material he buys 3 metres of shirt material. He sells the materials at 12 % and 10 % profit respectively. His total sale is Rs. 36,660. How much trouser material did he buy ?

Ans. Let ratio between shirt material and trouser material be

The cost of shirt material =

The selling price at 12% gain =

=

= =

= =

The cost of trouser material =

The selling price at 10% gain =

=

= =

= =

According to the question,

= 100 meters

Now, trouser material = =

= 200 metres

Hence, Hasan bought 200 metres of the trouser material.

8. Half of a herd of deer are grazing in the field and three fourths of the remaining are playing nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.

Ans. Let the total number of deer in the herd be

According to question,

Hence, the total number of deer in the herd is 72.

9. A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.

Ans. Let present age of granddaughter be years.

Therefore, Grandfather’s age = years

According to question,

years

Hence, granddaughter’s age = 6 years and grandfather’s age = = 60 years.

10. Aman’s age is three times his son’s age. Ten years ago he was five times his son’s age. Find their present ages.

Ans. Let the present age of Aman’s son be years.

Therefore, Aman’s age = years

According to question,

= 20 years

Hence, Aman’s son’s present age = 20 years

And Aman’s present age = = 60 years