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__START QUIZ__**Directions (1-5):**Two equations I and II are given below in each question. You have to solve these equations and give answer

**(a) if x<y**

**(b) if x>y**

**(c) if x≤y**

**(d) if x≥y**

**(e) if x**

**=**

**y or no relation can be established**

**Q1. I.**𝑥

^{2}−11𝑥+24=0

**II**. 2𝑦

^{2}−9𝑦+9=0

**Q2. I.**𝑥

^{2}−3481=0

**II.**3𝑦

^{2}=√2160003

**Q3. I.**x

^{2}−5x−14=0

**II.**y

^{2}+7y+10 = 0

**Q4. I.**5x

^{2}+2x−3=0

**II.**2y

^{2}+7y+6=0

**Q5. I.**(17)

^{2}+144 ÷18 = x

**II.**(26)

^{2}− 18 ×21 = y

**Q6.**Aman is 50% more efficient than Ravi while 20% more efficient than Mohan. If Ravi and Aman together can complete a work in 18 days, then in what time Ravi and Mohan can complete the same work if they work alternatively starting from Ravi ?

(a)
360/11

(b)
20

(c)
40

(d)
36

(e)
30

**Q7.**Investment of A is 40% more than investment of B. Ratio between time of investment of A and B is 2 : 3. If total investment of A and B is 6000 and profit of A obtained out of total profit is 16% less than his investment then find the difference between the profit earned by B and profit earned by A.

(a)
182

(b)
196

(c)
210

(d)
220

(e)
224

**Q8.**.‘A’ and ‘B’ started a business together. ‘A’ invested (P + 250) initially while ‘B’ invested ‘1.5P’ initially. ‘A’ invested Rs. 1000 more after every 4 months while ‘B’ invested Rs. 500 more after every quarter. After an year ‘A’ got 46% of total profit then find the amount invested by ‘B’ in 3

^{rd}quarter?

(a)
3300

(b)
3800

(c)
4300

(d)
4800

(e)
5300

**Q9.**‘C’ worked for all days till the work is completed. ‘B’ worked for first 12 days and then left and after 3 days ‘D’ joined ‘C’ and they worked till the work is completed. ‘A’ worked for last 20 days. Each man did equal share of work. If ‘A’ and ‘C’ together can complete the work in 48 days then in how many days ‘A’, ‘B’ and ‘D’ together can complete the work.

(a)
24 days

(b)
20 days

(c)
15 days

(d)
16

(e)
240/17 days

**Q10.**A, B and C entered into a partnership with some investment for one year. After one-year A got 2/5 profit and B and C got equal part of remaining profit. If total profit after one year is 15% instead of 10% then A got 900 Rs. more. Find the investment of B.

(a)
12000

(b)
45000

(c)
27000

(d)
18000

(e)
13500

**Solutions**

**S1. Ans.(d)**

**Sol.**I. 𝑥

^{2}−8𝑥−3𝑥+24=0

𝑥(𝑥−8)−3(𝑥−8)=0

𝑥=3, 8

II. 2𝑦

^{2}−6𝑦−3𝑦+9=0
2𝑦(𝑦−3)−3(𝑦−3)=0

𝑦=3, 3/2

∴ 𝑥≥𝑦

**S2. Ans.(e)**

**Sol.**

I.𝑥=±59 |II.3𝑦

^{2}=60⇒𝑦=±√20
∴ No relation exists.

**S3. Ans. (d)**

**Sol.**

I. 𝑥

^{2}−7𝑥+2𝑥−14=0
𝑥(𝑥−7)+2(𝑥−7)=0

𝑥=7,−2

II. y

^{2}+5y+2y+10 = 0
𝑦=−2,−5

𝑥≥y

**S4. Ans. (b)**

**Sol.**

I.
5𝑥

^{2}+5𝑥−3𝑥−3=0
5𝑥(𝑥+1)−3(𝑥+1)=0

𝑥=35,−1

II.
2𝑦

^{2}+4𝑦+3𝑦+6=0
2𝑦(𝑦+2)+3(𝑦+2)=0

𝑦=−3/2, −2

𝑥>𝑦

**S5. Ans.(a)**

**Sol.**

𝐼. x=289+ 144/18=297 | 𝐼𝐼. 𝑦=298

𝑥<𝑦

**S6. Ans.(c)**

**S7. Ans.(c)**

**S8. Ans.(c)**

**S9. Ans.(b)**

**S10. Ans.(e)**