#### Ques 1.

If the numerator of a fraction is increased by 150% and the denominator of the fraction is increased by 350%, the resultant fraction is 25/51 . What is the original fraction?

**Solution : **

⇒ Numerator increased 150% , So it becomes 100x+150x=250x

⇒ Denominator increased 350%, So it becomes 100y+350y=450y

⇒ (250x)/(450y) = 25/51

⇒ x/y = 15/17

#### Ques 2.

The ratio of the present ages of Anju and Sandhya is 13: 17. Four years ago the ratio of their ages was 11: 15. What will be the ratio of their ages six years hence?

**Solution :**

Present ages ratio =13:17

4 years ago ratio. = 11:15

⇒ Check ratios differences

13-11 = 2 ; 17-15 = 2 ( this is used when difference is equal, otherwise we need to convert ratios)

⇒ 2 parts ------- 4years

⇒ 13 parts ------ ?

Anju age = 26 years

2 parts ------- 4 years

17 parts ---- ?

⇒ Sandhya age = 34 years

⇒ After 6 years anju age = 26+6=32

⇒ Sandhya = 34+6 =40

⇒ After 6 years ratio = 32:40 = 4:5

#### Ques 3.

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is

**Solution:**

Rectangular perimeter = he covered distance in 8 minutes

⇒ 2 (3x+2x) = 12 *8 * 1000/60= 1600

⇒ 10x = 1600

⇒ x = 160

Length = 3x = 3* 160 = 480m

Breadth = 2x = 2 *160= 320m

⇒ Area = lb = 480*320= 153600 sq.m

#### Ques 4.

15, 25, 40, 65, ?, 195

**Solution :**

⇒ 15 x 2 = 30 -5 = 25

⇒ 25 x 2 = 50-10=40

⇒ 40 x 2 = 80-15 = 65

⇒ 65 x 2 = 130-20= 110

#### Ques 5.

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

**Solution :**

⇒ Time taken by "A" = 6days

⇒ Time taken by "B" = 8days

⇒ A,B and C are finished in 3 days

⇒ L.C.M of 6,8 and 3 = 24

⇒ Efficiency of "A" = 24/6 = 4

⇒Efficiency of " B" = 24/8= 3

⇒ Efficiency of "A+B+C" = 24/3 =8

⇒ 4+3+C = 8

⇒ C efficiency = 8-7= 1

Share of C = (1/8) x (3200) = 400

#### Ques 6.

I. 6x² - 49x+99=0.

II. 5y²+17y+14=0

find relation between X and Y?

**Solution :**

6x²-49x+99=0

⇒ (3x-11) (2x-9)=0

⇒ x=11/3, 9/2

5²+17y+14

⇒ (5y+7) (y+2)

⇒ y=-2,-7/5

x>y

#### Ques 7.

In how many different ways can the letters of the word BAKERY be arranged?

**Solution :**

Total Letters in word = 6

Possibility ways =6! = 720

#### Ques 8.

A cylindrical tank of diameter 35 cm is full of water. If 11 litres of water is drawn off, find in the water level in the tank?

**Solution :**

Cylinder volume= πr²h

= 22/7×35/2×35/2×h

= 11000

height = 80/7

#### Ques 9.

Mohan gave 25% of a certain amount of money to Ram. From the money Ram received, he spent 20% on buying books and 35% on buying a watch. After the mentioned expenses, Ram has rs 2700 remaining. How much did Mohan have initially?

**Solution :**

25%×45%=2700

100%=2700×100×100/25×45 = 24000

==> Mohan have initially = 24000

#### Ques 10.

A driver of auto rickshaw makes a profit of 20% on every trip when he carries 3 passengers and the price of petrol is Rs. 30 a litre. Find the % profit for the same journey if he goes for 4 passengers per trip and the price of petrol reduces to Rs. 24 litres? (revenue per passenger is same)

**Solution :**

cp=100

sp=120

after reduction

Let the auto requires 1 liter petrol per trip i.e 30rs,

profit per trip = 20*30/100 = 6 rs

Total fare per trip = 30+6=36rs

Fare per passenger = 36/3 = 12 rs

Fare for 4 passengers = 4*12 = 48rs

Profit per trip per liter(for petrol price rs 24) = 48-24= 24

profit % = 24*100/24 = 100%

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