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
⇒ 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
