#### Ques 1.

A dishonest shopkeeper makes cheating of 20% at the time of buying and 40% at the time of selling the goods. He promises to sell goods at 10% loss. Find profit percent.

**Solution :**

(120 x 100 )/60=200

⇒200x90/100 =180

⇒180-100=80%

#### Ques 2.

A group of men decided to do a job in 8 days. But since 10 men dropped out everyday, the job got completed at the end of 12th day. How many men were there at beginning?

**Solution :**

10 men left every day means 1+2+3+.....11

11×10=110 dropped

Total men=x

Job done= 8x

⇒ 8x= (x-110)×12

⇒ 8x= 12x- 12×110

⇒ 4x= 1320

⇒ x= 330

#### Ques 3.

Two pipes can separately fill a tank in 20 hrs and 30 hrs respectively. Both the pipes are opened to fill the tank but when the tank is one-third full a leak develops in the tank through which one-third of the water supplied by both the pipes leaks out. What is the total time taken to fill the tank?

**Solution :**

Two pipes separately takes 20hrs and 30hrs

L.C.M of 20, 30 = 60 = tank efficiency

A efficiency = 60/20=3

B efficiency= 60/30=2

1/3 of tank = 20

Time taken to fill 1/3 tank = 20/(2+3) = 4 hours

Remaining tank to be fill = 60-20= 40

Leak is 1/3 efficient of A and B = 1/3 x (3+2)= 5/3

⇒ Total efficiency of A,B and leak = 2+3-(5/3)= 10/3

Remaining tank filled in = (40)/(10/3)= 12 hours

⇒ Total time = 12+4=16 hours

#### Ques 4.

The ratio of length to the breadth of a rectangular plot is 8 : 7. If the perimeter of plot is 120 m. Find the area of the plot.

**Solution :**

Let length be 8x and that of breadth be 7x

⇒ 2 (8x + 7x) = 120

⇒ 30x = 120

⇒ x = 4

Area = (8*4)*(7*4) = 32× 28 = 896 m2

#### Ques 5.

38 men can do piece of work in 30 days. How many men will be required to do the same piece of work in 19 days?

**Solution :**

38*30=19*X

⇒ X= 60 men

#### Ques 6.

The present age of Sumit and Rishi are in the ratio of 5 : 2. And after 9 years ratio of their ages will be 13 : 7.What is the difference between their ages?

**Solution : **

⇒ (5x +9)/(2x+9)=13/7

⇒ X=6

Difference of ages = 3X= 3*6=18years

#### Ques 7.

The incomes of Aman and Bhusan are in the ratio 4 : 3 and their expenditures are in the ratio of 6 : 4. If each saves 2750,what is the income of Aman?

**Solution :**

Income ratio = 4x :3x

Expenditure ratio = 6y:4y

⇒ Savings are equal and its 2750

Amman savings = 4x-6y=2750 --- (i)

Bhusan savings = 3x-4y=2750

⇒ 4x-6y = 3x-4y

⇒ y = x/2. --- (ii)

Substitute (ii) in (i)

⇒ x = 2750

Amman income = 4x = 4*2750 = 11000

#### Ques 8.

In how many different ways can a committee of 6 members can be formed from 7 men and 5 women comprising 4 men and 2 women?

**Solution :**

Required number of ways = 7C4 × 5C2 = 350

#### Ques 9.

Shruti goes to college at 35 km/hr and reaches the collage 12 minutes late. Next time she goes to college at 42 km/hr and reaches the college 9 min earlier than the scheduled time. What is the distance between the college and her home?

**Solution : **

⇒ (x/35) - (x/42) =(12+9)/60

⇒ (7x)/(35*42) = 21/60

Distance X = 147/2 = 73.5 km

#### Ques 10.

A trader sells an article at a loss of 16%, but when he increases the selling price of the article by 1155 he earns a profit of 3.25% of the cost price. If he sells the same article for 7800, what is his profit percentage?

**Solution :**

⇒ Case -(i)

Cp = 100x. Sp = 84x. Profit = 16x

Case-(ii)

Cp = 100x. Sp= 84x+1155. Profit% = 3.25%

In this case ⇒ [(84x+115-100x)/(100x)] * 100= 3.25

⇒ X = 60

Cp = 100x =109*60 =6000

New Sp= 7800

Profit % = (1800/6000)*100 = 30%

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