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.
Ques:- If y/x = 1/3 and x + 2y = 10, then x is
Recent Answer : Added by L.Lalitha priya On 2022-05-17 08:56:35:
Given y/x = 1/3, x+2y =10
3y=x
Then substitute x=3y in x+2y=10
3y+2y=10
5y=10
y=2
Then substitute y=2 in x=3y
x=3*2
x=6
: x=6, y=2
Ques:- A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
Recent Answer : Added by Admin On 2022-09-28 17:11:47:
No of men employed = N
No of days to finish the work = 9 days
No of men after increase = (N + 10)
No of days to finish the work = 6 days
Equating mandays
9N = (N+10)*6
9N — 6N = 60
3N = 60
N = 20
No of men employed = 20
Ques:- Embarrassing day in your life?
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Ques:- 16.66% of A is y and B% of 30 is 21 then, what % of A is 42?
Ques:- If you found 10 million dollars that belongs to nobody, what would you do?
Recent Answer : Added by Prajapati mitesh On 2022-08-14 16:41:51:
I will try to find that person
Or give that bag to police ..
Ques:- When Arthur is as old as his father Hailey is now, he shall be 5 times as old as his son Clarke is now. By then, Clarke will be 8 times older than Arthur is now. The combined ages of Hailey and Arthur are 100 years. How old is Clarke?
Recent Answer : Added by Stephanie Brewer On 2022-01-08 16:07:12:
Clarke is 80 years old
Ques:- Find the odd man out:
16, 25, 36, 72, 144, 196, 225
A. 225
B. 196
C. 72
D. 36
Recent Answer : Added by Akshay Narayan Shetty On 2022-04-02 06:58:08:
72
Because it is not a square number
Ques:- A, B and C are entered into a partnership. A invested Rs.6500 for 6 months, B invested Rs.8400 for 5 months and C invested for Rs.10000 for 3 months. A is a working partner and gets 5% of the total profit for the same. Find the share of C in a total profit of Rs.7400.
Ques:- For how long you will be associated with the company?
Recent Answer : Added by DK BOSS On 2021-07-21 15:26:46:
“Since I’ve been working and gaining experience to get into this company, I’d like to stay a long time if I’m offered the job, since this is where I want to be. “ “As long as there’s a lot of work to do, then I’d be happy to stay for a long time. Since I’m a busybody, I like to being productive most of the time.”
Ques:- Where are you working at present?
Ques:- What are your Future Plans for company
Ques:- Tell me something about youself
Ques:- A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?
Recent Answer : Added by Admin On 2022-09-29 19:29:04:
Speed = (45×518)m/sec=252m/sec
Total distance covered = (360+140) m = 500 m.
∴Required time= 500×225sec = 40 sec.
Ques:- There are twelve consecutive flags at an equal interval of distance. A man passes the 8th flag in 8 seconds. How many more seconds will he take to pass the remaining 4 flags?
Recent Answer : Added by DK BOSS On 2021-07-17 06:40:10:
This is more logical …
Let the 1st flag 1 placed at the origin ….
in crossing 8 flags he traveled 7 distances….
s=d/t
=7/8
time for 4 flags t=(d/s)=4/(7/8)=(4*8)/7=4.5714285714285714285714285714286
Ques:- What are you most proud of?
Ques:- The cost of 16 pens and 8 pencils is Rs.352 and the cost of 4 pens and 4 pencils is Rs.96. Find the cost of each pen?
Recent Answer : Added by azeem ahamed On 2021-12-20 17:15:45:
20
Ques:- The smallest number of 5 digit beginning with 3 and ending with 5 will be
A. 31005
B. 30015
C. 30005
D. 30025
Recent Answer : Added by Deepa verma On 2022-03-09 16:31:33:
C
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Ques:- A sum of money is put out at compound interest for 2 years at 20%. It would fetch Rs.482 more if the interest were payable half-yearly, then it were pay able yearly. Find the sum.
Ques:- Why Switched to MBA after BCA?
Ques:- Two trains are moving in the same directions at 65 km/hr and 45 km/hr. The faster train crosses a man in slower train in 18 seconds. The length of the faster train is
A. 100 m
B. 120 m
C. 145 m
D. 180 m
Recent Answer : Added by Prashanth On 2022-11-10 16:31:44:
Relative speed =65-45km/hr
Relative speed=20km/hr
Convert to m/s
S=20*5/18
S=5.555
Length of the faster train =5.55555*18seconds
=100meters
Ques:- A heap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of Coconuts in the heap is?
Recent Answer : Added by MB On 2021-11-19 18:20:08:
13. One group of each = 2+3+5 = 10 and 1 remainder for each = 1+1+1 = 3. 10+3 = 13
Ques:- The sum of four consecutive even numbers is 36. Find the sum of the squares of these numbers?
Recent Answer : Added by Suriya.B On 2023-05-22 09:15:15:
6+8+10+10= 36
6²+8²+10²+12²=344
Ques:- Tell me about your ability to work under pressure.
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Ques:- A can swim & cross 50m(the length of swimming pool) in 2 min. B can swim & cross 50m in 2min 15sec. Every time when they meet a bell gong is struck. For 2000m how many bell sounds might be produced?
Recent Answer : Added by Admin On 2020-05-17 12:02:01:
If the bell rung when they r started is also counted then it
will be 5 otherwise 4
Ques:- 1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
Recent Answer : Added by Robert Blackwell On 2022-09-02 17:04:29:
That will depend heavily on when in the journey the 200 men join.
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.