**Dear Aspirants,**

**Q1. A man invested Rs. 9600 in two equal parts on SI for T years and (T + 2) years at the rates of 12.5% p.a and 16% p.a respectively. If the man got a total interest of Rs. 4272, then find the value of T.**

**Q2. Veer invested Rs. P at the rate of 15% p.a and Rs. (P + 800) at the rate of 8.5% p.a. If veer gets a total simple Interest of Rs. 4836 after two years, then find the value of (P + 800).**

**Q3. A man invested Rs. 8500 on SI at the rate of R% per annum. If ratio between rate of interest and time period is 4 : 1 and total interest received is Rs. 1360 then find the time for which the man invested his sum?
**

**Q4. Mr. Adarsh invested certain principal sum on SI and got 34% more amount after four years. Find the rate for which Adarsh invested his sum?
**

**Q5. A man invested his total saving into three different banks namely SBI, UBI and BOB in the ratio of 2 : 1 : 2 for two years. Rate of simple interest offered by SBI is 20%, UBI is 16% and BOB is 12%. If the simple interest received from SBI is Rs. 672 more than interest received from BOB. Find total interest received by the man from UBI after two years.
**

**Directions (6-10)- Given below is the table which shows the number of registered voters in 5 villages and ratio of male to female in those registered voters in the year 2016 **

**Note - **Some values are missing in the table, you have to calculate them if required to answer the question.

**Q6. What is the sum of total registered female voters from village A and B together if registered male voters in village A are 200/11% less than registered male voters from village B?
**

**Q7. If average of all registered voters from all villages is 18400 and ratio of all registered voters from village C to all registered voters from Village E is 10 : 13 then find the sum of registered male voters from village B and E together.**

**Q8. Registered females from village A and B are equal. If in an election, 20% votes polled by all registered voters of village A are declared invalid in which ratio of male invalid votes to female invalid votes is 5: 3. Then, valid votes casted by females of village A are what percent of total registered female voters of village B.**

**Q9. If total registered voters from village C are 100/9% more than total registered voters from village B then, find the ratio of total registered voters from village C to total registered voters from village D.**

**Q10. If next year, registered voters from village D, are increased by 100/3% while registered male voters are increased by 100/7% and total registered female voters in 2016 in village B are 12.5% less than registered female voters of village D in year 2017 then, find registered male voters of village D in the year 2016.**

**Directions (11-15): Solve the following equations and mark the correct option given below. **

**Q11. I. x² – 27x + 180 = 0 **

**II. y² – 7y = 60**

x² – 12x – 15x + 180 = 0

x (x – 12) –15(x – 12) = 0

(x – 15) (x – 12) = 0

x = 15, 12

II. y² – 7y – 60 = 0

y² – 12y + 5y – 60 = 0

y (y – 12) +5 (y – 12) = 0

(y + 5) (y – 12) = 0

y= -5, 12

⇒ x ≥ y

**Q12. I. x² – 59x + 868 = 0 **

**II. y² – 53y + 702 = 0**

x² – 28x – 31x + 868 = 0

x (x – 28) – 31 (x – 28) = 0

(x – 31) (x – 28) = 0

x = 28, 31

II. y² – 53y + 702 = 0

y² – 27y – 26y + 702 = 0

y (y – 27) – 26(y – 27) = 0

(y– 27) (y – 26) = 0

y = 26, 27

⇒ x > y

**Q13. I. 100x² – 120x + 32 = 0 **

**II. 10y² – 17y + 6 = 0**

100x² – 40x – 80x + 32 = 0

20x (5x – 2) – 16(5x – 2) = 0

(20x – 16) (5x – 2) = 0

x = 4/5, 2/5

II. 10y² – 17y + 6 = 0

10y² – 12y – 5y + 6 = 0

2y (5y – 6) – 1 (5y – 6) = 0

(2y – 1) (5y – 6) = 0

y = 1/2, 6/5

⇒ No relation

**Q14. I. 15x² – 22x + 8 = 0 **

**II. 12y² – 5y – 2 = 0**

15x² – 12x – 10x + 8 = 0

3x (5x – 4) –2 (5x – 4) = 0

(5x – 4) (3x– 2) = 0

x = 4/5, 2/3

II. 12y² – 5y – 2 = 0

12y² – 8y + 3y – 2 = 0

4y (3y – 2) + 1 (3y – 2) = 0

(4y + 1) (3y – 2) = 0

y = -1/4, 2/3

⇒ x ≥ y

**Q15. I. x² + 8x + 15 = 0 **

**II. y² – 2y – 8 = 0**

x² + 5x + 3x + 15 = 0

x (x + 5) + 3 (x+ 5) = 0

(x + 5) (x + 3) = 0

x = –5, –3

II. y² – 2y – 8 = 0

y² – 4y + 2y – 8 = 0

y (y – 4) + 2(y – 4) = 0

(y – 4) (y + 2) = 0

y= –2, 4

⇒ x < y