Directions (1-5): Solve the following equations and mark the correct option given below.

Q1. I. 6x² + 7x + 2 = 0

II. 3y² + 8y + 5 = 0

if x>y

if x≥y

if y>x

if y≥x

if x=y or no relation can be established

Q2. I. 7x² – 23x + 6 = 0

II. y² – 7y + 12 = 0

if x>y

if x≥y

if y>x

if y≥x

if x=y or no relation can be established

Q3. I. 5x² + 13x – 6 = 0

II. 2y² + 13y – 7 = 0

if x>y

if x≥y

if y>x

if y≥x

if x=y or no relation can be established

Q4. I. 4x + 3y = 4

II. 6x + 5y = 8

if x>y

if x≥y

if y>x

if y≥x

if x=y or no relation can be established

Q5. I. x² - 19x + 88 = 0

II. y² + y – 56 = 0

if x>y

if x≥y

if y>x

if y≥x

if x=y or no relation can be established

Q6. P, Q and R can complete a work in 12, 15 and 25 days respectively. They received Rs. 13,500 for the completion of work. P and Q started the work together but after 2 days, Q left the work and P left 7 days before the completion of the work. The remaining work is completed by R working for the last 5 days. Then, find the share of P.

Rs. 8100

Rs. 9500

Rs. 8550

Rs. 9000

Rs. 8800

Q7. The sum of the ages of mother and daughter is 65 years. 10 years ago the product of their ages was 5 times the age of mother at that time. Then find the ratio of the present age of mother to the present age of daughter(age of mother is greater than 30 years).

10 : 3

12 : 5

9 : 2

3 : 1

4 : 1

Q8. A shopkeeper after allowing two successive discounts of 20% and 16⅔% on the marked price, earns a profit of 25% on selling the book. Find the ratio of cost price to the marked price of a book ?

4 : 9

2 : 5

3 : 5

6 : 11

8 : 15

Q9. Two places Aurangabad and Ellora are 120 km apart. Two cyclists leave Ellora for Aurangabad such that second leaves 4 hours after the first. Both the cyclists arrive at Aurangabad at the same time. Find the time taken by the slower cyclist on the trip if the speed of one cyclist is 5 km/hr more than the other.

8 hr

10 hr

12 hr

15 hr

20 hr

Q10. A rectangular field of area 720 m² is to be fenced on three sides leaving a side of 24 m uncovered. Perimeter of another triangular shaped field is 1/3rd of the perimeter of rectangular shaped field. Find the area of the triangular shaped field if its all sides are equal.

48√3 m²

36√3 m²

48 m²

60 m²

None of the above

SOLUTIONS

1.A

2.D

3.E

4.C

5.A

6.D

7.A

8.E

9.C

10.B

Q1. I. 6x² + 7x + 2 = 0

II. 3y² + 8y + 5 = 0

if x>y

if x≥y

if y>x

if y≥x

if x=y or no relation can be established

Q2. I. 7x² – 23x + 6 = 0

II. y² – 7y + 12 = 0

if x>y

if x≥y

if y>x

if y≥x

if x=y or no relation can be established

Q3. I. 5x² + 13x – 6 = 0

II. 2y² + 13y – 7 = 0

if x>y

if x≥y

if y>x

if y≥x

if x=y or no relation can be established

Q4. I. 4x + 3y = 4

II. 6x + 5y = 8

if x>y

if x≥y

if y>x

if y≥x

if x=y or no relation can be established

Q5. I. x² - 19x + 88 = 0

II. y² + y – 56 = 0

if x>y

if x≥y

if y>x

if y≥x

if x=y or no relation can be established

Q6. P, Q and R can complete a work in 12, 15 and 25 days respectively. They received Rs. 13,500 for the completion of work. P and Q started the work together but after 2 days, Q left the work and P left 7 days before the completion of the work. The remaining work is completed by R working for the last 5 days. Then, find the share of P.

Rs. 8100

Rs. 9500

Rs. 8550

Rs. 9000

Rs. 8800

Q7. The sum of the ages of mother and daughter is 65 years. 10 years ago the product of their ages was 5 times the age of mother at that time. Then find the ratio of the present age of mother to the present age of daughter(age of mother is greater than 30 years).

10 : 3

12 : 5

9 : 2

3 : 1

4 : 1

Q8. A shopkeeper after allowing two successive discounts of 20% and 16⅔% on the marked price, earns a profit of 25% on selling the book. Find the ratio of cost price to the marked price of a book ?

4 : 9

2 : 5

3 : 5

6 : 11

8 : 15

Q9. Two places Aurangabad and Ellora are 120 km apart. Two cyclists leave Ellora for Aurangabad such that second leaves 4 hours after the first. Both the cyclists arrive at Aurangabad at the same time. Find the time taken by the slower cyclist on the trip if the speed of one cyclist is 5 km/hr more than the other.

8 hr

10 hr

12 hr

15 hr

20 hr

Q10. A rectangular field of area 720 m² is to be fenced on three sides leaving a side of 24 m uncovered. Perimeter of another triangular shaped field is 1/3rd of the perimeter of rectangular shaped field. Find the area of the triangular shaped field if its all sides are equal.

48√3 m²

36√3 m²

48 m²

60 m²

None of the above

SOLUTIONS

1.A

2.D

3.E

4.C

5.A

6.D

7.A

8.E

9.C

10.B

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