**Find solutions for all the questions at the end of each set:**

### Set A

1.A man travelled a certain distance by train at the rate of 25 kmph. and walked back at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, the distance was

(1) 25 km

(2) 30 km

(3) 20 km

(4) 15 km

2.The HCF of two numbers is 23 and the other two factors of their LCM are 13 and 14. The larger of two numbers is :

(1) 276

(2) 299

(3) 345

(4) 322

3.Out of 450 students of a school 325 play football, 175 play cricket and 50 neither play football nor cricket. How many students play both football and cricket?

(1) 50

(2) 100

(3) 75

(4) 225

4.A cistern 6 m long and 4 m wide. Contains water up to a depth of 1 m 25 cm. The total area of the wet surface is

(1) 55 m^2

(2) 53.5 m^2

(3) 50 m^2

(4) 49 m^2

5.Two trains of equal length take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?

(1) 16

(2) 15

(3) 12

(4) 10

6.A starts from a place P to go to a place Q. At the same time B starts from Q to P. If after meeting each other A and B took 4 and 9 hours more respectively to reach their destinations, the ratio of their speeds is

(1) 3 : 2

(2) 5 : 2

(3) 9 : 4

(4) 9 : 13

7.A man can row at 5 kmph. In still water. If the velocity of current is 1 kmph. and it takes him 1 hour to row to a place and come back, how far is the place?

(1) 2.5 km

(2) 3 km

(3) 2.4 km

(4) 3.6 km

8.A trader marked his goods at 20% above the cost price. He sold half the stock at the marked price, one quarter at a discount of 20% on the marked price and the rest at a discount of 40% on the marked price. His total gain is

(1) 2%

(2) 4.5%

(3) 13.5%

(4) 15%

9. The HCF of two numbers is 15 and their LCM is 300. If one of the number is 60,the other is :

(1) 50

(2) 75

(3) 65

(4) 100

10.In a family of 8 adults and some minors, the average consumption of rice per head per month is 10.8 kg; while the average consumption for adults is 15 kg per head and for and for minors it is 6 kg per head. The number of minors in the family is :

(1) 8

(2) 6

(3) 7

(4) 9

Answer and Solution:

1.(3)

Let the distance be x km.

Total time = 5 hours 48 minutes = 29/5 hours

so x/25 + x/4 = 29/5

=> x = 20 km

2.(4) Let the numbers be 23x and 23y where x and y are co-prime

So LCM = 23xy

As given,

23xy = 23*13*14

so x = 13, y = 14

so The largest number = 23y= 23*14 = 322

3.(2)

4.(4)Required total area = Area of four walls + area of base

= 2*1.25(6+4)+6*4

= 49m^2

5.(3)

When a train crosses a telegraph post,If covers its own length.

so Speed of first train = 120/10 = 12 m/s

Speed of second train = 120/15 = 8 m/s

Relative speed 12+8 = 20 m/s

Required time = 2*120/20 = 12 seconds

6.(1)

7.(3)Let the distance be x km.

Speed upstream = 5-1 = 4 kmph

Speed downstrean = 5+1 = 6 kmph

so x/6 + x/4 = 1

x = 2.4 km

8.(1)

9.(2)

10.(3)

Let number of minors be x.

According to the question,

(8*15+x*6)/(8+x) = 10.8

=> x = 7

**Find solutions for all the questions at the end of each set:**

### Set B

1.Two pipes can fill a cistern in 3 hours and 4 hours respectively and a waste pipe can empty it in 2 hours. If all the three pipes are kept open. Then the cistern will be filled in :

(1) 5 hours

(2) 8 hours

(3) 10 hours

(4) 12 hours

2.A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days, B had to leave and A alone completed the remaining work. The whole work was completed in :

(1) 10 days

(2) 8 days

(3) 12 days

(4) 15 days

3.An article is sold at a profit of 20%. If it had been sold at a profit of 25%, it would have fetched Rs. 35 more. The cost price of the article is :

(1) Rs. 650

(2) Rs. 700

(3) Rs. 750

(4) Rs. 800

4.A tradesman sold an article at a loss of 20%. If the selling price had been increased by Rs. 100, there would have been a gain of 5%. The cost price of the article was :

(1) Rs. 200

(2) Rs. 25

(3) Rs. 400

(4) Rs. 250

5.If the ratio of areas of two squares is 225 : 256, then the ratio of their perimeters is :

(1) 225 : 256

(2) 256 : 225

(3) 15 : 16

(4) 16 : 15

6.The percentage increase in the area of a rectangle, if each of its sides is increased by 20%, is :

(1) 40%

(2) 42%

(3) 44%

(4) 46%

7.A number is increased by 20% and then again by 20%. By what per cent should the increased number be reduced so as to get back the original number?

(1) 30(5/9)%

(2) 19(11/31)%

(3) 40%

(4) 44%

8.A boy, after giving away 80% of his pocket money to one companion and 6% of the remainder to another, has 47 paise left with him. How much pocket money did the boy have in the beginning?

(1) Rs. 2

(2) Rs. 2.50

(3) Rs. 5

(4) Rs. 10

9.If the compound interest on a sum for 2 years at 12(1/2)% per annum is Rs. 510, the simple interest on the same sum at the same rate for the same period of time is :

(1) Rs. 400

(2) Rs. 480

(3) Rs. 450

(4) Rs. 460

10.5 persons can prepare an admission list in 8 days working 7 hours a day. If 2 persons join them so as to complete the work in 4 days, they need to work per day for :

(1) 10 hours

(2) 9 hours

(3) 12 hours

(4) 8 hours

Answers and Solution:

1.(4)

Part of the cistern filled in 1 hour

= 1/3 +1/4 – 1/2

= 1/12

Hence ,the cistern will be filled in 12 hours.

2.(3)

Work done by(A+B) in 1 day = 1/15+1/10 = = 1/6

so (A+B)’s 2 days work 2/6 = 1/3

Remaining work = 1 – 1/3 = 2/3

This part is done by A alone

1 work is done by A in 15 days

so 2/3 work is done in 15*2/3= 10 days.

Required number of days= 12 days

3.(2)

Let the cost price be Rs.x

so 125% of x – 120% of x = 35

x = 700

4.(3)

Let C.P of article be Rs.x.

so 105% of x – 80% of x = 100

= 25% of x = 100

so x = 400

5.(3)

6.(3)

Net Effect = (20+20+(20*20)/100)%

= 44%

7.(1)

Let the number be 100.

After 20% increase,number = 120

number = 120*120/100 = 144

so percent decrease = 44/144*100 = 30(5/9)%

8.(2)

Let the boy had Rs.x

Money given to first companion = 80% of x = 4x/5

Remaining money = x – 4x/5 = x/5

Money given to another companion = 6/100*x/5 = 3x/250

Remaining money = x/5 – 3x/250

so 47x/250 = 47/100

x = Rs. 2.50

9.(2)

10.(1)

persons 7 : 5

:: 7 : x

Days 4 : 8

so 7 * 4 * X = 5*8*7

so x = 10 days