Ques:- A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:
Recent Answer : Added by shashank chourasiya On 2022-03-09 16:42:05:
Hint: Assume that the speed of the stream is x and the speed of the boat in still water is x. From the statement of the question form two equations in two variables x and y. This system is reducible to linear equations in two variables. Reduce the system to a system of linear equations in two variables by proper substitutions. Solve the system of equations using any one of the methods like Substitution method, elimination method, graphical method or using matrices. Hence find the value of x satisfying both the equation. The value of x will be the speed of the stream.
Complete step-by-step answer:
Let the speed of the stream be x, and the speed of the boat in still water be y.
We have the speed of the boat upstream = y-x.
Speed of the boat downstream = y+ x.
Now since it takes 14 hours to reach a place at a distance of 48 km and come back, we have the sum of the times taken to reach the place downstream and time taken to return back upstream is equal to 14.
Now, we know that time =Distance speed
Using, we get
Time taken to reach the place =48y+x and the time taken to return back =48y−x.
Hence, we have
48y+x+48y−x=14
Dividing both sides by 2, we get
24y+x+24y−x=7 —–(i)
Also, the time taken to cover 4km downstream is equal to the time taken to cover 3km upstream.
Hence, we have 4y+x=3y−x
Transposing the term on RHS to LHS, we get
4y+x−3y−x=0 ——– (ii)
Put 1y+x=t and 1y−x=u, we have
24t+24u=7 ——-(iii)4t−3u=0 ——–(iv)
Multiplying equation (iv) by 6 and subtracting from equation (iii), we get
24t−24t+24u+18u=7⇒42u=7
Dividing both sides by 42, we get
u=742=16
Substituting the value of u in equation (iv), we get
4t−3(16)=0⇒4t−12=0
Adding 12 on both sides, we get
4t=12
Dividing both sides by 4, we get
t=18
Reverting to original variables, we have
1y+x=18 and 1y−x=16
Taking reciprocals on both sides in both equations, we have
y+ x=8 ——- (v)y−x=6 ——–(vi)
Adding equation (v) and equation (vi), we get
2y=14
Dividing both sides by 2, we get
y=7.
Substituting the value of y in equation (v), we get
7+x=8
Subtracting 7 from both sides we get
x = 8-7 =1
Hence the speed of the stream is 1 km/hr.
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Ques:- What is happiness for you?
Ques:- Given 2 cubes,arrange any number from 0-9 so dat wen put together whole month dates should appear.
Ques:- Grass in lawn grows equally thick and in a uniform rate. It takes 24 days for 70 cows and 60 days for 30 cows to eat the whole of the grass. How many cows are needed to eat the grass in 96 days?
Recent Answer : Added by Admin On 2020-05-17 12:01:01:
Use 3pt. Formula
( (x-x1)/(x2-x1) )=( (y-y1)/(y2-y1) )
We get 150
Ques:- If you have a chance to purchase shares of company will you purchase or not
Ques:- Why do you want to switch over to this company?
Ques:- The radius of a cylindrical vessel is 7cm and height is 3cm. Find the whole surface of the cylinder?
Recent Answer : Added by Pavan On 2021-10-12 12:52:36:
2* pi* r ( h + r )
r=3cm
h=7cm
2 * 22/7 *7 ( 10 ) = 440 sq cm
Ques:- In a knockout tournament 51 teams participated. A team is out if the tournament if the team lost twice. How many matches to be held to choose the winner?
Recent Answer : Added by DK BOSS On 2021-07-17 06:18:22:
ans : 101 bcoz after every two matches one team is eliminated…so to eliminate 50 team there will be require 100 matches…+ 1 for deciding winner…
Ques:- What is the toughest problem you've had to face, and how did you overcome it?
Ques:- What motivates you?
Ques:- Given n red balls and m blue balls and some containers, how would you distribute those balls among the containers such that the probability of picking a red ball is maximized, assuming that the user randomly chooses a container and then randomly picks a ball from that?
Ques:- Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
Recent Answer : Added by mv On 2021-08-14 13:06:15:
1261
Ques:- 30% apples out of 450 are rotten. How many apples are in good condition?
A. 180
B. 240
C. 315
D. 335
Recent Answer : Added by Venu On 2022-08-14 16:44:44:
450÷100×30=135
450-135=315
Ans: 315
Ques:- Why you want to leave your job?
Ques:- Why might you be successful in such a job?
Ques:- Number Series 7,16,9,15,11,14,?
Recent Answer : Added by Admin On 2020-05-17 12:01:30:
First nos series is 7,9,11,?
ie odd number siries ie 7,9,11,13
Second number series is 16,15,14
ie 1 less the previous number 16,15,14,13
Ans —-series is 7,16,9,15,11,14,13,13
Ques:- The LCM of 148 and 185 is
A. 3700
B. 2960
C. 740
D. 680
Recent Answer : Added by R.Geethanjali On 2022-04-02 06:59:22:
740
Ques:- Can you share your salary expectations?
Ques:- The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?
Recent Answer : Added by Ponranjithkumar J On 2022-05-17 09:08:41:
answer is 28
>2+8=10
>reverse of 28 is 82
>subtract 28 from 82
>82-28=54
the number is 28
Ques:- What is your educational qualification, experience, etc.
Ques:- A/B = 3/5 15A = ?
Recent Answer : Added by Admin On 2020-05-17 11:59:28:
5A=3B,
*3 SO,
15A=9B
Ques:- Two varieties of wheat – A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
Recent Answer : Added by Mohamed Raja M On 2022-04-02 07:00:53:
answer = 16.5Rs
A=3*9=27Rs
B=7*15=105Rs
132 R for 10 kg
therefore,
1kg amount = 132/10=13.2 so,
5kg mixture price = 13.2*5=66Rs
mixture will sell 25%profit then the price =66*(25/10)=33/2=16.5Rs
Ques:- What is the extent of your participation in major reports that have to be written?
Ques:- There are two candles of equal lengths and of different thickness. The thicker one lasts of six hours. The thinner 2 hours less than the thicker one. Ramesh lights the two candles at the same time. When he went to bed he saw the thicker one is twice the length of the thinner one. How long ago did Ramesh light the two candles?
Recent Answer : Added by Naru Mani Chandan On 2022-03-18 09:18:12:
3 hours ago.
Thin candle melts 3/4 in 3 hours leaving 1/4
Where as in the same time thick candle melts 3/6 leaving 3/6 which is 1/2. Now thick candle is exactly twice than the thin candle.
Or via modeling:
We need to find time at which the length of the thin candle is half the thick candle. Let x be the time. Thin candle melts at 1/4 an hour and thick candle melts at 1/6 an hour. In x hours they melt at x/4 and x/6 respectively. What’s left will be 1 – x/4 and 1 – x/6. We need to find x at which :
2 * (1 – (x/4)) = 1 – (x/6)
This equation results in x = 3
Ques:- A clock takes 9 seconds to strike 4 times. In order to strike 12 times at the same rate, the time taken is
A. 27 seconds
B. 29 seconds
C. 33 seconds
D. 36 seconds
Recent Answer : Added by Mad On 2021-11-22 17:29:36:
9 sec=4 times
x sec=12 times
x=(9*12)/4=27 sec
Ques:- What was the name of first bank established in India ?
Recent Answer : Added by shubham On 2022-04-02 06:57:58:
bank of calcutta originated in 1806
there is another answer such as
bank of hindustan
Ques:- Can you explain in one line why should we select you fromthe number of applications we have received?
Ques:- Distance between two poles is 50 meters. A train goes by 48 at a speed of kmph. In one minute how many poles will be crossed by the train ?
Recent Answer : Added by Admin On 2020-05-17 12:01:58:
16 poles per min
48kmph=48000 meters per hr
=800 meters per min
800/50=16 poles per min
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Hint: Assume that the speed of the stream is x and the speed of the boat in still water is x. From the statement of the question form two equations in two variables x and y. This system is reducible to linear equations in two variables. Reduce the system to a system of linear equations in two variables by proper substitutions. Solve the system of equations using any one of the methods like Substitution method, elimination method, graphical method or using matrices. Hence find the value of x satisfying both the equation. The value of x will be the speed of the stream.
Complete step-by-step answer:
Let the speed of the stream be x, and the speed of the boat in still water be y.
We have the speed of the boat upstream = y-x.
Speed of the boat downstream = y+ x.
Now since it takes 14 hours to reach a place at a distance of 48 km and come back, we have the sum of the times taken to reach the place downstream and time taken to return back upstream is equal to 14.
Now, we know that time =Distance speed
Using, we get
Time taken to reach the place =48y+x and the time taken to return back =48y−x.
Hence, we have
48y+x+48y−x=14
Dividing both sides by 2, we get
24y+x+24y−x=7 —–(i)
Also, the time taken to cover 4km downstream is equal to the time taken to cover 3km upstream.
Hence, we have 4y+x=3y−x
Transposing the term on RHS to LHS, we get
4y+x−3y−x=0 ——– (ii)
Put 1y+x=t and 1y−x=u, we have
24t+24u=7 ——-(iii)4t−3u=0 ——–(iv)
Multiplying equation (iv) by 6 and subtracting from equation (iii), we get
24t−24t+24u+18u=7⇒42u=7
Dividing both sides by 42, we get
u=742=16
Substituting the value of u in equation (iv), we get
4t−3(16)=0⇒4t−12=0
Adding 12 on both sides, we get
4t=12
Dividing both sides by 4, we get
t=18
Reverting to original variables, we have
1y+x=18 and 1y−x=16
Taking reciprocals on both sides in both equations, we have
y+ x=8 ——- (v)y−x=6 ——–(vi)
Adding equation (v) and equation (vi), we get
2y=14
Dividing both sides by 2, we get
y=7.
Substituting the value of y in equation (v), we get
7+x=8
Subtracting 7 from both sides we get
x = 8-7 =1
Hence the speed of the stream is 1 km/hr.