#### Ques 1.

**4725,1050,300,120,80,? **

**Solution :**

4725 / 4.5=1050

1050/3.5=300

300/2.5=120

120/1.5=80

80/0.5=160

#### Ques 2.

**I. 2a^2 − 11a + 12 = 0**

II. 35b^2 − 18b − 8 = 0

**Solution :**

==>2a^2-8a-3a+12 =0

==>2a(a-4)-3(a-4)=0

==> a = 4, 3/2

==> 35b^2-28b+10b-8=0

==> 7b(5b-4)+2(5b-4) =0

==> b = -2/7 , 4/5

**a>b**

#### Ques 3.

**P takes 10 days more than Q to complete a piece of work. If both of them can complete the work in 6(2/3 )days, in how many days can P alone complete the work?**

**Solution :**

Q takes x days and P takes x+10 days

Both are completed the work = (1/x)+(1/x+10) = 20/3

==> 3x^2-10x-200=0

==> x = 10, -20/3

Days cant be negative sign . so X = 10

P alone completed = 10+10=20 days

#### Ques 4.

**What approximate value should come in place of the question mark (?) in the following questions.** **25.675% of 1321 + 64.328% of 4001= ?**

**Solution :**

==> 25/100 * 1320 + 64/100 *4000

==> 330+2560 = 2890

#### Ques 5.

**The difference between the simple interest received from two different sources on Rs. 1500 for 3 years is Rs. 13.50. The difference between their rate of interest is**

**Solution :**

[1500 x R1 x 3] /100 – [1500 x R2 x 3] /100 =13.5

==>4500 (R1 – R2) = 1350

==>R1 – R2 =1350/4500=0.30%

#### Ques 6.

**The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P. What will be the ratio of the ages of P and Q after 4 years?**

**Solution :**

Present age Ratio = 6:7

Difference = 7-6 = 1

1 unit ----- 4 years

6 units ---- 24years

7 units ---- 28 years

after 4 years P and Q age = 28 years and 32 years

Ratio = 28:32= 7:8

#### Ques 7.

**The average score of 11 matches is 50. If the average score of first 6 matches is 49 and that of last 6 is 52, find the sixth match score?**

**Solution :**

Total score in 11 matches = 11*50 =550

First 6 matches total score = 6*49= 294

Last 6 matches total score = 6*52 = 312

6th match score = (294+312)-550=56

#### Ques 8.

**The Simple interest on a certain sum for 2 years at 10% per annum is Rs. 90. The corresponding compound interest is?**

**Solution :**

P = 90*100/(2*10) = 450

C.I = 450(1+(10/100))^2 - 450= 450 * 121/100 - 450 = 94.5

#### Ques 9.

**A box contain 10 Black balls, 7 White balls and 12 Red balls. A ball is drawn at random. What is the probability that the ball drawn is either Black or White ?**

**Solution :**

Total no of balls =10+7+12 = 29

Probability of Black balls =10/29

Probability of White balls = 7/29

Probability of Either Black or White = 10/29 + 7/29 = 17/29

#### Ques 10.

The salaries of P,Q and R are in the ratio 5:3:2.If the increments of 20% ,10% and 20% are allowed in their salaries, then what will be the new ratio of their salaries ?

**Solution :**P,Q and R salaries Ratio = 5:3:2 = 500:300:200

If P Salary Increases 20% = 500×(20/100) = 100 => 500+100 = 600

If Q Salary Increases 10% = 300×(10/100) = 30 => 300+33 = 330

If R Salary Increases 20% = 200×(20/100) = 40 => 200+40 = 240

New Ratios = 600:330:240 = 20:11:8

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