Chapter 4: Linear Equations in One Variable

Solution:-

The denominator of a rational number is greater than the numerator by 10. If the numerator is increased by 1 and the denominator is decreased by 1, then the expression for the new denominator is x + 9.

Let us assume numerator be x,

So, denominator = x + 10

Rational number = x/(x + 10)

As per the condition given in the question, the numerator is increased by 1 and the denominator is decreased by 1.

New rational number = Numerator + 1/ (denominator – 1)

= (x + 1)/(x + 10 – 1)

= (x + 1)/(x + 9)

∴the new denominator is x + 9.

Solution:-

The sum of two consecutive multiples of 10 is 210. The smaller multiple is 100.

Let us assume the two consecutive multiples of 10 be 10x and 10x + 10.

So,

Sum of two consecutive multiples of 10 = 10x + 10x + 10 = 210

20x + 10 = 210

20x = 210 – 10

20x = 200

x = 200/20

x = 10

∴the two consecutive multiples of 10 are 10x = 10 × 10 = 100

10x + 10 = (10 × 10) + 10

= 110

Hence, the smaller multiple of 10 is 100.

In questions 33 to 48, state whether the statements are true (T) or false (F).

Solution:-

False.

Because, His age 2 years ago was (y + 1) years.

Solution:-

False.

Given,

Shikha’s present age is p years

Reemu’s present age is 4 times the present age of Shikha = 4p

After 5 years Reemu’s age will be = (4p + 5)

Solution:-

False.

From the question it is given that,

The unit’s place digit is = x

Sum of two digits = 9

Then,

Ten’s digit = 9 – x

So,

The number = 10 (9 – x) + x

= 90 – 10x + x

= 90 – 9x

Solution:-

True.

From the question it is given that,

Anju’s present age = y years

Present age of Anju’s mother = (65 – y) years

Then,

Before 5 years, Anju’s mother age = 65 – y – 5

= (60 – y) years

Solution:-

False.

Let us assume number of boys be 5y and the number of girls be 4y.

From the question,

5x – 4x = 9

X = 9

∴Number of boys = 5x = 5 × 9 = 45 boys

Number of girls = 4x = 4 × 9 = 36 girls.

Solution:-

True.

Let us assume age of A be y years.

So, age of B = (90 – y) years.

Then,

Before 5 years A’s age = (x – 5) years

and B’s age = (90 – x – 5) = (85 – x) years.

Solution:-

False.

Two different equations can have the same answer

For example: – (i) 4x + 2 = 3

4x = 3 – 2

X = ¼

(ii) 4x – 6 = – 5

4x = – 5 + 6

X = ¼

Solution:-

False.

Given, 3x – 3 = 9

Transposing –3 to RHS it becomes 3

3x = 9 + 3

3x = 12