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

### Set A

1.Two persons A and B started from two different places towards each other. If the ratio of their speeds b 3 : 5, then what is the ratio of distance covered by A and B respectively till the point of meeting?

(a) 1 : 2

(b) 3 :4

(c) 3 : 5

(d) 5 : 3

2.A is twice fast as B and B thrice as fast C. the journey covered by C in 78 minutes will be covered by A in:

(a) 12 min

(c) 13 min

(c) 15. 5 min

(d) none of these

3.Two persons, Atif and Laila start at the same time from Allahabad and Lucknow and proceed towards each other at 45 km/h and 54 km/h respectively. When they meet, it is found that one of them has travelled 72 km more than the other. The distance between the places (in km) is:

(a) 729

(b) 792

(c) 540

(d) none of these

4.A man covers a certain distance by his own car. Had he moved 6 km/h faster he would have taken 4 hours less. If he had moved 4 km/h slower, he would have taken 4 hours more. The distance (in km) is:

(a) 240 km

(b) 640 km

(c) 480 km

(d) none of these

5.A train 200 m long travels at the speed of 72 km/h. A man is running at 3.6 km/h in the same direction in which the train is going. The train will pass the man in:

(a) 10 s

(b) 12 3/19 s

(c) 10 10/19 s

(d) none of these

6.Two trains A and B start simultaneously in the opposite direction from two points P and Q arrive at their destinations 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 km/h per hour:

(a) 90 km/h

(b) 160 km/h

(c) 67.5 km/h

(d) none of these

7.A man travels the first part of his journey at 20 km/h and the next a 70 km/hr, covering the entire journey at an average speed of 50 km/hr. What is the ratio of the distance that he covered at 20 km/h to that he covered at 70 km/h?

(a) 4 : 21

(b) 3 :22

(c) 1 : 4

(d) 3 : 5

8.A train met with an accident 120 km from station A. It completed the remaining journey at 5/6 of its previous speed and reached 2 hours late at station B. Had the accident taken place 300 km further, it would have been only 1 hour late? What is the speed of the train?

(a) 100 km/h

(b) 120 km/h

(c) 60 km/h

(d) 50 km/h

9.A boat covers 48 km upstream and 72 km downstream in 12 hours, while it covers 72 km upstream and 48 km downstream in 13 hours. The speed of stream is:

(a) 2 km/h

(b) 2.2 km/h

(c) 2.5 km/h

(d) 4 km/h

10.Mallah can row 40 km upstream and 55 km downstream in 13 h and 30 km upstream and 44 km downstream in 10 hours. What is the speed of Mallah in still water?

(a) 6 km/h

(b) 12 km/h

(c) 3 km/h

(d) 8 km/h

Answers Solution:

1.(c) when time is constant the distances covered by A and B will be in the ratio of their speeds, respectively.

2.(b) The ratio of speeds of A, B, C = 6 : 3 : 1

so The ratio of time taken by A, B, C = 1 : 2 : 6

so Time taken by A = 13 min

3.(b) 9 km difference arises in the 99 km distance.

so 72 km difference will arise in the 792 km distance.

4(c)

5.(c)Time = length of train/Relative speed

= 200/19 = 10 10/19 s

6.(b) S1/S2 = √(t2/t1 )

=> 120/S2 = √(9/16)=3/4

S2 = 160 km/h

7.(a)

8.(c)

9.(a) Let the downstream speed be D and upstream speed by U, then

=> 48/U+72/D = 12

and 48/D+72/U = 13

so 48m + 72n = 12 ……..(i)

and 48n + 72m = 13 ………(ii)

Solving Eq. (i) and (ii), we get

m + n = 5/24 and m – n = 1/24

so D = 12 km/h and U = 8km/h

so Speed of current = 2 km/h

10.(d)

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

### Set B

1.A train passes a platform in 36 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is

A. None of these

B. 280 meter

C. 240 meter

D. 200 meter

2.A train , having a length of 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train

A. 10 sec

B. 8 sec

C. 6 sec

D.4 sec

3.Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?

A.5/11

B.6/11

C.7/11

D.8/11

4.A boat covers a certain distance downstream in 4 hours but takes 6 hours to return upstream to the starting point. If the speed of the stream be 3 km/hr, find the speed of the boat in still water

A. 15 km/hr

B. 12 km/hr

C. 13 km/hr

D. 14 km/hr

5.The number of employees in Companies A, B and C are in a ratio of 4 : 5 : 6 respectively. If the number of employees in the three Companies is increased by 25%, 30% and 50% respectively, what will be the new ratio of employees working in Companies A, B and C respectively ?

A.13 : 10 : 18

B. 10 : 13 : 17

C. 13 : 15 : 18

D.None of these

6.When 3626 is divided by the square of a number and the answer so obtained is multiplied by 32, the final answer obtained is 2368. What is the number ?

A.7

B.36

C.49

D.6

7.A and B invest in a business in the ratio 3: 2. Assume that 5% of the total profit goes to charity. If A’s share is Rs. 855, what is the total profit?

A. 1400

B. 1500

C. 1600

D. 1200

8.A Bus runs at the speed of 50 kms per hour when not serviced and runs at 60 kms/hr. when serviced. After servicing the Bus covers a certain distance in 6 hours. How much time will the Bus take to cover the same distance when not serviced ?

A. 8·2 hours

B. 6·5 hours

C.8 hours

D. 7·2 hours

9.A Seller has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?

A.Rs. 4991

B.Rs. 5991

C.Rs. 6001

D.Rs. 6991

10.If a sum of money trebles itself in 40 years,what is the rate of interest?

A. 5%

B. 6%

C. 4%

D. None of these

1.(C)Explanation :

Speed of the train = 54 km/hr

= (54×10)/36 m/s

= 15 m/s

Length of the train = speed × time taken to cross the man = 15×20 = 300 m

Let the length of the platform = L

Time taken to cross the platform = (300+L)/15

=> (300+L)/15 = 36

=> 300+L = 15×36 = 540

=> L = 540-300 = 240 meter

2(C)Explanation :

Distance = 110 m

Relative speed = 60+6 = 66 kmph (Since both the train and the man are in moving in opposite direction)

= 66×10/36 mps = 110/6 mps

Time = distance/speed = 110/(110/6) = 6 s

3(B)Explanation:

Part filled by (A + B + C) in 3 minutes = 3(1/30+1/20+1/10)= (3×11/60)= 11/20

Part filled by C in 3 minutes = 3/10 .

so Required ratio = (3/10 x 20/11) = 6/11

4(A)Explanation :

Let the speed of the water in still water = x

Given that speed of the stream = 3 kmph

Speed downstream = (x+3) kmph

Speed upstream = (x-3) kmph

He travels a certain distance downstream in 4 hour and come back in 6 hour.

ie, distance travelled downstream in 4 hour = distance travelled upstream in 6 hour

since distance = speed × time, we have

(x+3)4=(x−3)6

=> (x + 3)2 = (x – 3)3

=> 2x + 6 = 3x – 9

=> x = 6+9 = 15 kmph

5.(D)

6.(A)

7.(B)Explanation :

Assume that the total profit is x.

Since 5% goes for charity, 95% of x will be divided between A and B in the ratio 3: 2

=> A’s profit = (95x/100) * (3/5) = 855

=> 95x/100 = 855*5/3 = 285*5 = 1425

=> x = 1425 * 100/95 = 285 * 100/19 = 1500

Hence the total profit = 1500

8.(D)

9.(A)Explanation:

Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.

Required sale = Rs. [ (6500 x 6) – 34009 ]

= Rs. (39000 – 34009)

= Rs. 4991.

10.(A)

Let the sum of money be Rs.x

After 40 years, this becomes 3x

Simple Interest = 3x – x = 2x

Simple Interest = PRT/100

=2x=x×R×40/100

2=R×40/100

200=40R

R=5%

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

### Set C

1.Rs. 864 is divided among A, B and C such that 8 times A’s share is equal to 12 times B’s share and also equal to 6 times C’s share. How much did B get?

(a) Rs. 399

(b) Rs. 192

(c) Rs. 288

(d) Rs. 72

2.A, B and C entered into a business and their investments ratio was 5 : 4 : 3. After 4 months B invested Rs. 1,000 more and after 8 months C invested Rs. 2, 000 more. At the end of one year the profit ratio was 15 : 14 : 11, then the investment of C at the beginning was

(a) Rs. 3000

(b) Rs. 6000

(c) Rs. 4500

(d) Rs. 7500

3.A, B and C rent a pasture. A puts in 10 oxen for 7 months, B 12 oxen for 5 months and C 15 oxen for 3 months for grazing . If the rent of the pasture is Rs. 175/-, how much must C pay as his share of rent?

(a) Rs. 45

(b) Rs. 50

(c) Rs. 55

(d) Rs. 60

4.A, B, and C started a business with their investments in the ratio 1 : 2: 4. After 6 months A increased his capital by 50% and B invested twice the amount as before while C withdraw 1/4 of his own investment. The ratio of their profits at the end of the year was

(a) 10 : 5 : 9

(b) 5 : 12 : 14

(c) 6 : 9 : 17

(d) 5 : 14 : 16

5.A starts business with Rs. 3500/- and after 5 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is B’s contribution in the capital?

(a) Rs. 8000

(b) Rs. 8500

(c) Rs. 9000

(d) Rs. 7500

6.A number is divided into two parts in such a way that 80% of 1st part is 3 more than 60% of 2nd part and 80% of 2nd part is 6 more than 90% of the 1st part. Then the number is.

(a) 125

(b) 130

(c) 135

(d) 145

7.A. B and C enter into a partnership. A invests Rs. 2400 for 4 years, B Rs. 2800 for 8 years and C Rs. 2000 for 10 years. They earn Rs. 1 170. Find the share of each.

(1) Rs. 420

(2) Rs 540

(3) Rs. 108

(4) Rs. 216

8.A, B and C enter into partnership with capital contribution of Rs. 25,000, Rs. 30,000 and Rs.15,000 respectively. A is the working partner and he gets 30% of the profit for managing the business. The balance proﬁt is distributed in proportion to the capital investment. At the year-end, A gets Rs. 200 more than Band C together. Find the total proﬁt.

(1) Rs. 2500

(2) Rs. 2000

(3) Rs. 2200

(4) Rs. 9.400

9.A, B and C enter into a partner ship. Their capital contribution is in the ratio 21 : 18 : 14. At the end of the business term they share proﬁts in the ratio 15 : 8 :9. Find the ratio of time for which they invest their capitals.

(1)37 : 38 : 72

(2) 39 : 38 : 72

(3) 90 : 56 : 81

(4) None of these

10.A, B and C enter into a partnership. Their contributions are Rs.30 lakhs, Rs. 20 lakhs, and Rs.10 lakhs respectively. A and B are working partner while C is a sleeping partner. A and B get 10% and 15% of gross profit respectively as salary for managing the business. If at the year end C receives Rs. 3.75 lakhs,as proﬁt, ﬁnd the share of A.

(1) Rs. l6 Lakhs

(2) Rs. 12 Lakhs

(3) Rs. 18 Lakhs

(4) Rs. 20 Lakhs

ANSWERS AND SOLUTION

1.(b) 8A = B * 12 = 6C

=> 8A/24 = 12B/24 = 6C/24

=> A/3 = B/2 = C/4

so A : B : C = 3 : 2 : 4

so B’s share = 2/(3 + 2 + 4) * 864

= 2/9 * 864 = Rs. 192

2.(a) Initial investment :

A = Rs. 5x

B= Rs. 4x

C = Rs. 3x

so Ratio of their equivalent capitals for 1 month

= 5x * 12 : (4x * 4 + (4x + 1000) * 8) : (3x 8 + (3x + 2000) * 4)

= 15x : (12x + 2000) : 9x + 2000)

so 15x/(12x + 2000) = 15/14

=> 14x = 12x + 2000

=> 2x = 2000

x = Rs. 1000

3.(a) Share of rent = (number of oxen * time)

A : B : C

= (10 * 7) : (12 * 5) : (15 * 30)

A : B : C = 70 : 60 : 45

A : B : C = 14 : 12 : 9

C’s share of rent

= 9/(14 + 12 + 9) * 175

= 9/35 * 175 = 45

so C’s share of rent is Rs. 45

4.(b) Ratio of equivalent capital of A, B and C for 1 month

= (x * 6 + 3x/2 * 6) : (2x * 6 + 4x * 6) : (4x * 6 + 3x * 6)

= 15x : 36x : 42x

= 5 : 12 : 14

5.(c) A’s investment of Rs. 3500 is for 12 months

B’s investment (let it be Rs. x) is for 7 months only.

At the end of the year the profit is divided in the ratio 2 : 3 and

it must be equal to the ratio of the product. (Amount x time)

12 * 3500/ 7x = 2/3

Or, x = 12 * 3500/7 * 3/2

Or. X = 9000

6.(c)

7.(d) This is a case of compound partnership.

Rs. 2400 investment for 4 years earns as much as Rs. 2400 * 4 = Rs. 9600 in 1 year

Similarly, Rs. 2800 for 8 years is equivalent to Rs. 2800 * 8 = Rs. 22400 in 1 year

Rs. 2000 for 10 year is equivalent to Rs. 2000 * 10 = Rs. 20,000 in 1 year

The profit is, therefore, divided in the ratio

Rs.9600: Rs.22400: Rs.20000

or 12 : 28 : 25

Sum of the ratio = 12 + 28 + 25 = 65

Rs. 1170/65 = Rs. 18

So, A’s share = 12 * Rs. 18 = Rs. 216

8.(b)

9.(c) Ratio of profits = Ratio of capital multiplied by time.

so Ratio of time = Ratio of profits divided by respective capitals.

= 15/21 : 8/18 : 9/14

= 5/7 : 4/9 : 9/14 = 90/126 : 56/126 : 81/126

[126 is LCM of 7, 9 and 14]

A : B : C = 90 : 56 : 81.

10.(c)