#### Ques 1.

*A reduction of 20% in the price of ghee enables a person to get 5.2 kg more for 130Rs. What is the original price of ghee per kg ?*

**Solution :**

130*20/100=26/5.2=5

==>5*100/80=6.25

#### Ques 2.

*A container contains 80 litres of milk , From this container 16 litres of milk was taken out and replaced by water . This action was repeated one more time. What is the amount of milk in container after second replacement?*

**Solution :**

Remaining solution = initial quantity (1 - (taken quantity/initial quantity))^ number of times

Remaining quantity= 80(1-(16/80))^2 = 51.2 liters

#### Ques 3.

*A card is drawn from a pack of playing cards, what is the probability of getting either a black or a black queen?*

**Solution :**

= (26C1+2C1)/52C1

= 14/26=7/13

#### Ques 4.

*The square of a number is greater than 22 times the same number by 48. What is the number ?*

**Solution :**

X^2 = 22X+48

==> X^2-22X-48=0

==>X=24

#### Ques 5.

*The average weight of 32 students of a class was 48.5kg. After 10 new students joined the class, its average weight increased by 2.75kg. What is the average weight of 10 new students who joined the class?*

**Solution :**

Total Weight of 10 members = (2.75×32) + (51.25×10)

Average Of weight of 10 members = 600.5/10=60.05kg

#### Ques 6.

*A shopkeeper bought two varieties of rice , the first 20kgs at Rs 30 per kg and the other 25kgs at Rs 36 per kg .After mixing the two varieties of rice , at what should he sell the mixed to gain 20% profit ?*

**Solution : **

==>(30*20)+(30*25)/45=100/3

100% ------ 100/3

120% ------ X

Selling Price = 40

#### Ques 7.

*A boat can travel 12.6km DownStream in 18 minutes and 8.25km upstream in 15 minutes. What is the speed of the current ?*

**Solution :**

DownStream speed = (12.6*60)/18=42kmph

Upstream Speed = (8.25*60)/15 = 33kmph

speed of current = (42-33)/2 = 4.5kmph

**Solution :**

18-14=4

14-12=2

12-4 = 8

4-2 = 2

2-X = 12

X = -10

Answer = -10

#### Ques 9.

*At a discount of 10% of the entire purchase Ram could have bought 1 more kg of sugar by paying only 5% of the original amount more. How many kilograms of sugar has Ram bought?*

**Solution :**

CP = 100

After 10% discount= 100*90/100% = 90

Now he pays 5% more on actual selling = 100*105% = 105

1kg cost = (105-90) = 15

Total kgs = 90/15 = 6kgs

#### Ques 10.

*I. 2x^2-11x+12=0* *II. 2y^2-17y+36=0*

**Solution :**

2x^2-11x+12

=>x=3/2,4

2y^2-17y+36

=> y=4,9/2

**x ≤ y**

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