Monday, 29 December 2014

Quant Quiz on Boats and Streams with concepts

Boats and Streams

Let us know what is Downstream and what is Upstream. Because these concepts are the heart of Boats and Streams.

Downstream : In water,the direction along the stream is called downstream. I mean, If a boat or a swimmer swims in the same direction as the stream, then it is called downstream. Obviously the boat or swimmer require less efforts to travel using downstream. Because the stream itself helps the objects to move.

Remember, as the object moves along with the water, the stream helps the object.

So, the down stream speed (DS) is

DS = U+V

where U is the speed of the object in the still (calm) water

V is the speed of the water.

Upstream : If the boat or the swimmer is swimming in the opposite direction in which the stream is passing is called upstream. In simple words, the direction against the stream is called upstream.

Remember, as the object moves against the water pushes the object in opposite direction.

So, the upstream speed (US) is

US = U-V

where U is the speed of the object in the still (calm) water

V is the speed of the water.

Important Formulas on Boats and Streams :

Let us assume that the speed of the boat in still water is U km/hr and the speed of stream is V km/hr then, as mentioned above :

Speed downstream = (u+v)km/hr

Speed upstream = (u-v)km/hr

èIf the speed downstream is a km/hr and the speed upstream is b km/hr then :

Speed in still water = 1/2(a+b) km/hr

Rate of stream = 1/2(a-b)km/hr

Questions : -

1. A boat can run 13 km/hr in still water and the speed of current 4 km/hr. in how many hours the boat will covered 68 km down streams?

(1) 2 hours (2) 3 hours

(3) 4 hours (4) 5 hours

2. A man rows downstream 32 km and 14 km upstream. If he takes 6 hours to cover each distance, then the Velocity (in km/h) of current is:

(1) 1/2 (2) 3/2

(3) 2 (4) 5/2

3. A man can row at 5 km/h 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) 1.5 km (2) 2.4 km

(3) 3.5 km (4) 1 km

4. A man can row 40 km upstream and 55 km downstream in 13 hours. Also, he can row 30 km upstream and 44 km downstream in 10 hours. Find the speed of the man in still water and the speed of the current.

(1) 5 (2) 3

(3) 6 (4) 4

5. In a stream running at 2 km/h, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water.

(1) 22 km/hr (2) 20 km/hr

(3) 25 km/hr (4) 18 km/hr

6. A man takes 3 hours 45 minutes to row a boat I5 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the river current in km/hr.

(1) 1 km/hr (2) 2 km/hr

(3) 3 km/hr (4) 4 km/hr

7. A person can row a boat d km upstream and the same distance downstream in 5 hours 15 minutes. Also, he can row the boat 2d km upstream in 7 hours. How long will it take to row the same distance 2d km downstream?

(1) 3/2 hours (2) 7 hours

(3) 7 (¼) (4) 7/2 hours

8. A man swimming in a stream which flows 1.5 km/h, finds that in a given time he can swim twice as fast with the stream as he can against it. At what rate does he swim?

(1) 4 km/hr (2) 4.5 km/hr

(3) 6 km/hr (4) 7 km/hr

9. A motorboat in still water travels at a sped of 36 km/h. It goes 56 km upstream in 1 hour 45 minutes. The time taken by it to cover the same distance down the stream will be:

(1) 2 hours 25 minutes (2) 3 hours

(3) 1 hour 24 minutes (4) 2 hours 21 minutes

10. A man can row 6 km/h in still water. If the speed of the current is 2 km/h, it takes 3 hours more in upstream than in the downstream for the same distance.

(1) 30 km (2) 24 km

(3) 20 km (4) 32 km

ANSWER WITH EXPLANATION:

1. (3)

The speed downstream = 13+4 = 17 km/hr

∴Time taken to covered 68 km = 68/17 = 4 hours

2. (2)

Rate downstream = 32/6 km/h; Rate upstream = 14/6 km/h

Velocity of current = 1/2 (32/6 - 14/6) km/h

= 3/2 km/h

3. (2)

-Speed downstream = (5 + 1) km/h = 6 km/h.

Speed upstream = (5 – 1) km/h = 4 km/h.

Let the required distance be x km.

Then, x/6 + x/4 = 1

2x + 3x = 12

5x = 12

x = 2.4 km.

4. (2)

Let rate upstream = x km / hr and rate downstream = y km / hr.

Then, 40/x+ 55/y =13 ...(i)

and 30/x+44/y=10 ...(ii)

Multiplying (ii) by 4 and (i) by 3 and subtracting, we get :

11/y=1 or y=11.

Substituting y = 11 in (j), we get : x = 5.
\threrefore Rate in still water =1/2(11+5) km/h=8km/h.

Rateofcurrent = 1/2(11−5) km/h=3km/h.

5. (1)

Let the speed of the motorboat in still water be x km/h. Then,
Speed downstream = (x + 2) km/h; Speed upstream = (x - 2) km/h.
6/x+2+6/x−2 = 33/60

<=> 11x2−242x+2x−44=0

«=> (x - 22) (11x + 2) = 0 <=> x = 22. Hence, speed of motorboat in still water = 22 km/h.

6. (1)
Rate downstream=15334 km/hr

=15×415km/hr=4km/hr.

Rate upstream=(5212) km/hr

=(5×25)=2km/hr

Speed of current=12(4−2)km/hr=1km/hr.

7. (4)

Let the speeds of boat and stream be x and y km/hr respectively.

Then, Rate downstream = (x + y) km/hr and Rate upstream = (x - y) km/hr

Given d / (x+y) + d / ( x-y ) =5 hrs 15 minutes = 21/4 hours

and 2d / (x+y) = 7 => d / (x+y)=7/4 => 2d / (x+y)=7/2

Hence, he takes 7/2 hours to row 2d km distance downstream.

8. (2)

Rate of stream =1.5 km/hr

Let speed of man in still water = x km/hr and Distance = d

Upstream speed = (x - 1.5) km/hr Downstream speed = (x + 1.5) km/hr

Given, 2d / (x+1.5) = d/ (x-1.5) => 2x - 3 = x + 1.5 => x = 4.5 km/hr

9. (3)

Speed of the motorboat upstream

= 56km/1 ¾ hours

=32 km/h

Let the speed of the current = x km/h

36 – x = 32

à 36 – 32 = 4 km/h

speed of motorboat downstream = 36 + 4 = 40 km/h

Time taken to cover 56 km at 40 km/h = 56/40 = 7/5 hours

= 1 hour 24 minutes

10. (2)

Let he required distance be x km.

x/6-2 + x/ 6 + 2 = 3

à x/4 – x/8 = 3

à 2x –x/8 = 3

= x=3 x 8 = 24 km.

Give your answer in the comment section along with your timing and judge where you stand in the competition.

Saturday, 27 December 2014

Time and Work - Complex Problems (Part-2)

1)A and B undertake to do a piece of workfor Rs 600.A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they can finish it in 3 days, Find the share of each?
a.Rs 50
b.Rs 75
c.Rs.100
d.Rs.150

2)A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work?
a.30 days
b.40 days
c.50 days
d.60 days

3)P,Q and R are three typists who working simultaneously can type 216 pages in 4 hours In one hour , R can type as many pages more than Q as Q can type more than P. During a period of five hours, R can type as many pages as P can during seven hours. How many pages does each of them type per hour?
a.x=15,y=18, and z=21
b.x=15,y=21, and z=21
c.x=18,y=18, and z=21
d. x=15,y=18, and z=15

4)Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
a.6 hours
b.8 hours
c.10 hours
d. 12 hours

5)Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both working together. If B worked alone, he would need 4 1/2 hours more to compete the job than they both working together. What time would they take to do the work together.
a.3 days
b.4 days
c.5days
d.6 days

6)A and B can do a work in12 days, B and C in 15 days, C and A in 20 days. If A,B and C work together, they will complete the work in how many days?
a.8 days
b.5 days
c.10 days
d.12 days

7)A and B can do a work in 8 days, B and C can do the same wor in 12 days. A,B and C together can finish it in 6 days. A and C together will do it in how many days?
a.8 days
b.5 days
c.10 days
d.12 days

8)A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in how many days?
a.80 days
b.50 days
c.25 days
d.12 days

9) A is thrice as good a workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
a.45 days
b.45/2 days
c.20 days
d.12 days

10) A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how much time will A&B, working together, finish the work?
a.80 days
b.30 days
c.20 days
d.12 days

Answers :

Sol 1: C's one day's work=(1/3)-(1/6+1/8)=1/24
Therefore, A:B:C= Ratio of their one day’s work=1/6:1/8:1/24=4:3:1
A's share=Rs (600*4/8)=300
B's share= Rs (600*3/8)=225
C's share=Rs[600-(300+225)]=Rs 75

Sol 2: Work done by A in 10 days=10/80=1/8
Remaining work=(1-(1/8))=7/8
Now, work will be done by B in 42 days.
Whole work will be done by B in (42*8/7)=48 days
Therefore, A's one day's work=1/80
B’s one day's work=1/48
(A+B)'s one day's work=1/80+1/48=8/240=1/30
Hence, both will finish the work in 30 days.

Sol 3 :Let the number of pages typed in one hour by P, Q and R be x,y and z
respectively
Then x+y+z=216/4=54 ---------------1
z-y=y-x => 2y=x+z -----------2
5z=7x => x=5x/7 ---------------3
Solving 1,2 and 3 we get x=15,y=18, and z=21

Sol 4: Number of pages typed by Ronald in one hour=32/6=16/3
Number of pages typed by Elan in one hour=40/5=8
Number of pages typed by both in one hour=((16/3)+8)=40/3
Time taken by both to type 110 pages=110*3/40=8 hours.

Sol 5: (1/(x+8))+(1/(x+(9/2)))=1/x
=>(1/(x+8))+(2/(2x+9))=1/x
=> x(4x+25)=(x+8)(2x+9)
=> 2x2 =72
=> x2 = 36
=> x=6
Therefore, A and B together can do the work in 6 days.

Sol 6: (A+B)'s one day's work=1/12;
(B+C)'s one day's work=1/15;
(A+C)'s one day's work=1/20;
Adding we get 2(A+B+C)'s one day's work=1/12+1/15+1/20=12/60=1/5
(A+B+C)'s one day work=1/10
So, A,B,and C together can complete the work in 10 days.

Sol 7: (A+B+C)'s one day's work=1/6;
(A+B)'s one day's work=1/8;
(B+C)'s one day's work=1/12;
(A+C)'s one day's work=2(A+B+C)'s one day's work-((A+B)'s one day
work+(B+C)'s one day work)
= (2/6)-(1/8+1/12)
=(1/3)- (5/24)
=3/24
=1/8
So, A and C together will do the work in 8 days.

Sol 8: (A+B)'s one day's work=1/10;
C's one day's work=1/50
(A+B+C)'s one day's work=(1/10+1/50)=6/50=3/25
Also, A's one day's work=(B+C)’s one day's work
From i and ii ,we get :2*(A's one day's work)=3/25
=> A's one day's work=3/50
B's one day’s work=(1/10-3/50)
=2/50
=1/25
B alone could complete the work in 25 days.

Sol 9: Ratio of times taken by A and B=1:3.
If difference of time is 2 days , B takes 3 days
If difference of time is 60 days, B takes (3*60/2)=90 days
So, A takes 30 days to do the work=1/90
A's one day's work=1/30;
B's one day's work=1/90;
(A+B)'s one day's work=1/30+1/90=4/90=2/45
Therefore, A&B together can do the work in 45/2days

Sol 10: Work Done by A n 10 days =10/80=1/8
Remaining work =1-1/8=7/8
Now 7/8 work is done by B in 42 days
Whole work will be done by B in 42*8/7= 48 days
=> A's one day's work =1/80 and
B's one day's work =1/48
(A+B)'s one day's work = 1/80+1/48 = 8/240 = 1/30
Hence both will finish the work in 30 days.

Click Here for the Time and Work (Part-1)

Thursday, 25 December 2014

Quant Quiz

1.A sum of Rs 731 is distributed among A, B and C, such that A receives 25% more than B and B receives 25% less than C. What is C’s share in the amount?
(1)Rs 172
(2)Rs 200
(3)Rs262
(4)Rs 272

2.Manoj sold an article for Rs 15000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price?
(1)Rs12,500
(2)Rs13,500
(3)Rs12,250
(4)Rs13,250

3.What will be the compound interest accrued on an amount of Rs 10,000 @20p.c.p.a. in two years if the interest is compounded half-yearly?
(1)Rs4,400
(2)Rs4,600
(3)Rs4,641
(4)Rs 4,680

4.A committee of 3 members is to be selected out of 3 men and 2 women. What is the probability that the committee has at least 1 woman?
(1)1⁄10
(2)9⁄20
(3)9⁄10
(4)1⁄20

5.B and C together can complete a piece of work in 8 days. A and B can complete the same work in 12 days and A and C can complete the same work in 16 days. In how many days can A, B and C together can complete the work?
(1)3 3⁄9
(2)7 5⁄13
(3)7 5⁄12
(4)3 5⁄12

6.The average speed of a car is 1 4⁄5 times the average speed of the bus. A tractor covers 575km in 23 hours. How much distance the car cover in 4 hours of the speed of the bus is twice the speed of the tractor?
(1)340km
(2)480km
(3)360km
(4)450 km

7.A pump can fill a tank with water in 2 hours. Because of the leak, it took 2 1⁄3 hours to fill the tank. The leak can drain all the water of the tank in:
(1)4 1⁄3 hours
(2)7hours
(3)8 hours
(4)14 hours

8.A shopkeeper mixed two verities of rice at Rs. 20/kg and Rs. 30/kg in the ratio 2 : 3 and sell the mixture at 10% profit. Find the price per kg at which he sold the mixture?
(1)Rs.26
(2)Rs.28.8
(3)Rs.28
(4)Rs.28.6

9.The ratio of the present ages of Anju and Sandhya is 13:17 respectively. Four years ago the ratio of their respective ages was 11:15. What will be the respective ratio of their ages six years hence?
(1)3:4
(2)7:8
(3)4:5
(4)6:5

10.A shopkeeper bought 30kg of wheat at the rate of Rs45 per kg. He sold 40% of the total quantity at the rate of Rs50 per kg. Approximately, at what price per kg should he sell the remaining quantity to make a profit of 25% overall?
(1)Rs54
(2)Rs52
(3)Rs60
(4)Rs56

Answers With Explanations:

1. (4)
Let C's share be Rs x.
Then, B gets =0.75 x.
A gets = 1.25×0.75x
x+0.75x+0.9375x=731
2.6875x=731
x=731⁄2.6875 =272

2. (1)
SP=Rs15000
SP after 10% discount= 15000-10%of15000= 15000-1500=Rs13500
Profit on SP= 8%
CP= 13500⁄108 ×100=Rs 12500

3. (3)
CI=10000[{(11⁄10 )×(11⁄10 )×(11⁄10 )×(11⁄10 )}-1]
4.(3)
Probability that the committee has at least one woman
= 1-P(no. of woman in the committee)
= 1-P(all men in the committee)
=1-1⁄10 =9⁄10

5. (2)
(B+C)'s 1 day work= 1⁄8 ...(i)
(A+B)'s 1 day's work= 1⁄12 ...(ii)
(A+C)'s 1 day's work = 1⁄16 ...(iii)
On adding all these three equations,
2(A+B+C)'s one day's work = 1⁄8 +1⁄12 1⁄16 =(6+4+3)⁄48 =13⁄48
(A+B+C)'s one day's work= 13⁄96
∴A, B and C can complete the work in 96⁄13 =7 5⁄13

6. (3)
Speed of the tractor= distance/ time
=575⁄23 =25kmph
∴speed of bus= 50kmph
∴speed of car= 9⁄5 ×50=90kmph
∴distance covered by the car in 4 hours= 4×90=360km

7. (4)
Work done by the leak in 1 hour = (1⁄2 -3⁄7 )=1⁄14
∴leak will empty the tank in 14 hours.

8. (4)
CP of mixture = (20*2+30*3)⁄2+3 =26
SP of the mixture = 1.1×26=28.6

9.(3)
Let the present ages of Anju and Sandhya be 13x and 17x years respectively.
∴13x-4⁄17x-4 =11⁄15
=>187x-44=195x-60
=>195x-187x=60-40
=>x=2
∴Required ratio= (13×2+6):(17×2+6)
=4:5

10.(3)
CP of wheat= 30×45=Rs1350
40% of 30kg =12kg
SP of 12kg = 12×50 = Rs 600
For 25% profit, total SP of all the wheat is 1350×125⁄100 =Rs 1687.5
Remaining wheat (30-12)= 8kg
Rate of remaining wheat = 1087.5⁄18 ≈Rs60