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**Ques 1: Show that x = 4 is a solution of the equation**: **Solution:** Substituting x = 4 in

Since, LHS = RHS

âˆ´ x = 4 is a solution of the given equation.

**Ques 2:** **Solve**

**Solution:** We have

LCM of 3, 5, 2 and 4 is 60.

âˆ´ The given equation can be expressed as:

â‡’

â‡’

â‡’

â‡’

Thus, x = 27/10 is the required solution.

**Ques 3:** **Solve for **

**Solution: **We have

â‡’

â‡’

â‡’ 3x â€“ 4 + 44 â€“ 4x â€“ 3 = 2x + 4

â‡’ 3x â€“ 4x â€“ 2x = 4 + 3 â€“ 44 + 4

â‡’ 3x â€“ 6x = 11 â€“ 44

â‡’ â€“3x = â€“33 â‡’ x = 11

**Ques 4: Solve for**

**Solution: **We have

By cross multiplication, we get:

(2 + x)(7 â€“ x) = (5 â€“ x)(4 + x)

â‡’ 2(7 â€“ x) + x(7 â€“ x) = 5(4 + x) â€“ x(4 + x)

â‡’ 14 â€“ 2x + 7x â€“ x^{2} = 20 + 5x â€“ 4x â€“ x^{2}

â‡’ â€“x^{2} + x^{2} â€“ 2x + 7x â€“ 5x + 4x = 20 â€“ 14

â‡’ â€“7x + 7x + 4x = 6

â‡’ 4x = 6 â‡’ x = 6/4 or 3/2

Thus, the solution of the given equation is x = 3/2

**Ques 5:** **A number is such that it is as much greater than 65 as it is less than 91. Find the number.****Solution: **Let the number be x.

Since, we have [The number] â€“ 65 = 91 â€“ [The number]

â‡’ x â€“ 65 = 91 â€“ x

â‡’ x + x = 91 + 65

â‡’ 2x = 156

â‡’ x = 156/2 = 78

Thus, the required number is 78.

**Ques 6: The numerator of a fraction is 2 less than the denominator. If 1 is added to its denominator, it becomes 1/2. Find the fraction.****Solution:** Let the denominator of the fraction be x.

âˆ´ Numerator = x â€“ 2

The fraction =

Since, it becomes 1/2

When 1 is added to its denominator.

i.e

By cross multiplication, we have

2(x â€“ 2) = x + 1

â‡’ 2x â€“ 4 = x + 1

â‡’ 2x â€“ x = 1 + 4

â‡’ x = 5

â‡’ Fraction =

**Ques 7:** **After 24 years I shall be 3 times as old as I was 4 years ago. Find my present age.****Solution: **Let my present age be x years.

âˆ´ After 24 years, my age will be (x + 24) years.

4 years ago, my age was (x â€“ 4) years.

According to the given condition, we have

(x + 24) = 3(x â€“ 4)

â‡’ x + 24 = 3x â€“ 12

â‡’ x â€“ 3x = â€“12 â€“ 24

â‡’ â€“2x = â€“36

â‡’ x = -36/-2 = 18

Thus, my present age is 18 years.

**Ques 8:** **If the sum of two numbers is 30 and their ratio is 2 : 3, then find the numbers.****Solution:** Let one of the numbers be x.

âˆ´ The other number = (30 â€“ x)

According to the condition, we have

[âˆµ The ratio number is 2 : 3]

â‡’ 3x = 2(30 â€“ x) [By cross multiplication]

â‡’ 3x = 60 â€“ 2x

â‡’ 3x + 2x = 60

â‡’ 5x = 60

â‡’ x = 60/5 = 12

âˆ´ 30 â€“ x = 30 â€“ 12 = 18

Thus, the required numbers are 12 and 18.

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