**Directions (1-4): What approximate value should come in the place of question mark (?) in the following questions?**

**Q1. 6245.998 ÷ 18.01 × 39.88 = ? ÷ 25.089 × 40.01**

(a) 8675

(b) 8275

(c) 9675

(d) 8075

(e) 7975

**Q2. 19.85% of 1540 + 13.899% of 1050 = 20% of ?**

(a) 3175

(b) 2975

(c) 1875

(d) 2275

(e) 1675

**Q3. 958.08 × 779.98 ÷ 24.01 = ?**

(a) 30067.5

(b) 3942.5

(c) 30098.5

(d) 31342.5

(e) 31135

**Q4. 377.98 ÷ 8.93 + 123.94 ÷ 8.01 + 1460 × 1.25 = ?**

(a) 2945.5

(b) 2872.5

(c) 2882.5

(d) 1882.5

(e) 2688.5

**Q5. In a regular week, there are 6 working days for each day the working hours are seven. A man gets Rs. 80 per hour for regular work and Rs. 100 per hour for over time. If he earns Rs. 30,880 in 8 weeks, then for how many hours does he work?**

(a) 330 hours

(b) 376 hours

(c) 296 hours

(d) 384 hours

(e) 288 hours

**Q6. Two men together start a journey in the same direction. They travel 24 and 36 km per day respectively. After travelling of 6 days the man at 24 km per day doubles his speed and both of them finish the journey in the same time. Find the number of days taken by them to reach the destination.**

(a) 10 days

(b) 6 days

(c) 8 days

(d) 14 days

(e) 12 days

**Q7. The income of Roshan and Surbhi are in the ratio 9 : 4 and their ratio of expenditure is 7 : 3. If each saves Rs. 5000, what is the sum of their expenditure?**

(a) Rs. 215000

(b) Rs. 225000

(c) Rs. 250000

(d) Rs. 245000

(e) Rs. 275000

**Q8. P, Q and R invest in a business. If the ratio of their time period are 3 : 4 : 5 and their profits are in the ratio 5 : 6 : 8. Find the ratio in which the investment are made by P, Q and R.**

(a) 50 : 45 : 48

(b) 51 : 45 : 47

(c) 51 : 46 : 48

(d) 50 : 45 : 47

(e) 50 : 47 : 48

**Q9. If the price of commodity be raised by 18 (2/3) %, find by how much percent must a householder reduce his consumption of that commodity, so as not to increase his expenditure?**

(a) 14%

(b) 15.73%

(c) 12%

(d) 13.25%

(e) 16.43%

**Q10. Ten years ago, Anushka was thrice as old as Abhishek was, but 14 years hence, Anushka will be only twice as old as Abhishek. Find the present age of Anushka.**

(a) 72 years

(b) 80 years

(c) 78 years

(d) 76 years

(e) 82 years

**Directions (11-15): In each of these questions, two equations numbered I and II with variables x and y are given. You have to solve both the equations to find the value of x and y.**

**Q11.**

**I. 12x**

^{2}**– 59x + 72 = 0**

**II. 8y**

^{2}**– 58y + 99 = 0**

(a) if x > y

(b) if x >= y

(c) if x < y

(d) if x <= y

(e) if x = y or
relationship between x and y cannot be determined.

**Q12.**

**I. x**

^{2}**+ x – 20 = 0**

**II. y**

^{2}**+ 13y + 40 = 0**

(a) if x > y

(b) if x >= y

(c) if x < y

(d) if x <= y

(e) if x = y or
relationship between x and y cannot be determined.

**Q13.**

**I. x**

^{2}**+ 12x + 36 = 0**

**II. 5y**

^{2}**– 2 √15y + 3 = 0**

(a) if x > y

(b) if x >= y

(c) if x < y

(d) if x <= y

(e) if x = y or
relationship between x and y cannot be determined.

**Q14.**

**I. 10x**

^{2}**– 29x – 21 = 0**

**II. y**

^{2}**+ 13y – 68 = 0**

(a) if x > y

(b) if x >= y

(c) if x < y

(d) if x <= y

(e) if x = y or
relationship between x and y cannot be determined.

**Q15.**

**I. 72x**

^{2}**– 163x + 88 = 0**

**II. 56y**

^{2}**– 187y + 156 = 0**

(a) if x > y

(b) if x >= y

(c) if x < y

(d) if x <= y

(e) if x = y or
relationship between x and y cannot be determined.

**Solutions**

**S1. Ans.(a)**

**Sol. 6246/18 * 40 = ? / 25 * 40**

**? = 8675**

**S2. Ans.(d)**

**Sol. 20% * 1540 + 14% * 1050 = 20% * ?**

**? = (308 + 147)/0.2**

**? = 2275**

**S3. Ans.(e)**

**Sol. 958 * 780 / 24 = 31135**

**S4. Ans.(d)**

**Sol. 378/9 + 124/8 + 1460*1.25 = 42 + 15.5 + 1825 = 1882.5**

**S5. Ans.(b)**

**Sol. Let the man works overtime for x hours**

**Now, working hours in 8 weeks**

**= 8 × 6 × 7 = 336 hours**

**336 × 80 + x × 100 = 30880**

**100x = 30880 – 26880 = 4000**

**x = 40**

**Total hours = 336 + 40 = 376 hours**

**S6. Ans.(e)**

**Sol. Distance travelled by 1st man in 6 days**

**D1 = 24 × 6 = 144 km**

**and by 2nd man**

**D2 = 36 × 6 = 216 km**

**Let the total distance be x km**

**For remaining distance, let both take t days to reach the final destination**

**x – 144 = 2 × 24 t**

**x – 144 = 48 t -- (i)**

**and x – 216 = 36 t -- (ii)**

**from (i) and (ii), we get**

**Then, x – 144 – x + 216 = 48t – 36t**

**72 = 12 t**

**t = 6 days**

**Total days = 6 + 6 = 12 days**

**S7. Ans.(c)**

**Sol. Roshan’s saving =**

**9x – 7y = 5000**

**Surbhi’s savings =**

**4x – 3y = 5000**

**So, y = 25000**

**Total expenditure = 7y + 3y = 10y = 10 * 25000 = Rs. 250000**

**S8. Ans.(a)**

**Sol. Ratio of their investment**

**= 5/3 : 6/4 : 8/5**

**= 5/3 : 3/2 : 8/5**

**= 50 : 45 : 48**

**S9. Ans.(b)**

**Sol. Required reduction in consumption**

**= 56/3 * 1/(100 + 56/3) * 100**

**= 56/3 * 3/356 * 100 = 15.73%**

**S10. Ans.(e)**

**Sol. Let the age of Anushka = x and Abhishek = y**

**(x-10) = 3(y-10)**

**And, (x+14) = 2(y+14)**

**Y = 34, x = 82**

**S11. Ans.(c)**

**Sol. I. 12x**

^{2}– 32x – 27x + 72 = 0**(3x – 8) (4x – 9) = 0**

**x = 8/3, 9/4**

**II. 8y**

^{2}– 22y – 36y + 99 = 0**(2y – 9) (4y – 11) = 0**

**y = 9/2, 11/4**

**x < y**

**S12. Ans.(b)**

**Sol. I. x**

^{2}+ 5x – 4x – 20 = 0**(x – 4) (x + 5) = 0**

**x = 4, –5**

**II. y**

^{2}+ 5y + 8y + 40 = 0**(y + 8) (y + 5) = 0**

**y = –8, – 5**

**x >= y**

**S13. Ans.(c)**

**Sol. I. (x + 6)**

^{2}= 0**x = –6**

**II. 2**

**(√ 5y – √ 3)**

^{2}= 0**y = √ 3/ √ 5**

**x < y**

**S14. Ans.(e)**

**Sol. I. 10x**

^{2}– 35x + 6x – 21 = 0**(5x + 3) (2x – 7) = 0**

**x = –3/5, 7/2**

**II. y**

^{2}+ 17y – 4y – 68 = 0**(y – 4) (y + 17) = 0**

**y = 4, – 17**

**No relationship between x and y exists.**

**S15. Ans.(c)**

**Sol. I. 72x**

^{2 }– 64x – 99x + 88 = 0**(8x – 11) (9x – 8) = 0**

**x = 11/8, 8/9**

**II. 56y**

^{2}– 91y – 96y + 156 = 0**(7y – 12) (8y – 13) = 0**

**y = 12/7, 13/8**

**x < y**