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 the 3 digit number AB9 is a perfect square then is A an odd digit?
Recent Answer : Added by Shitoshe Wangatia On 2021-12-11 15:07:15:
A perfect square is a square number of a digit. eg 64 is a perfect number, a square of 8
Now digits AB9 is a square number of a number.
AB9 Can also be written as A multiply by B multiply by 9
Get the Square root of AB9
Assumption, A=1, B=1
1*1=1=A, 1*1=1=B Therefore,
Square root of A = A, B = B and 9=3
Therefore
An odd number is a number indivisible by 2.
for example 1,3,5,7…….
Therefore Squares A*B*9= AB9
Where a=1, b=1, 3 as digits.
Conclusion
A=1 is an odd number
Ques:- Which state in India has the largest coastline?
A. Orissa
B. Gujarat
C. Tamilnadu
D. Andhra Pradesh
Recent Answer : Added by Parth Satish Laturia On 2022-08-14 16:44:46:
gujarat
Ques:- How do you keep yourself updated about your current job and the HR industry?
Recent Answer : Added by DK BOSS On 2021-07-30 16:29:48:
I keep myself connected to social networking sites, the first platform for any technological advancement news and also keep surfing on the latest technology on the internet”. You can even say that you are connected to professional people from different media and have a continuing conversation with them regarding the growing technologies.
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 Arpan On 2022-05-17 09:08:01:
4.5
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Ques:- If time at this moment is 9 P.M., what will be the time 23999999992 hours later?
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Ques:- A and B can do a work in 12 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together?
Ques:- . Who was the Chairman of drafting Committee to prepare adraft Constitution for India?(1) Dr. S. Radha Krishnan(2) Dr. B.R. Ambedkar(3) K.M. Munshi(4) B.N. Roy
Ques:- You should be 100% genuine in every answer?
Ques:- If the area of the sqaure is increased by 69 % how much the length of the side will increase?
Recent Answer : Added by Admin On 2020-05-17 12:02:33:
30%
suppose the area is 100 and it was increased by 69%, then
the area is 169 which it indicates the side of the square
is 13.. which means 30% increase in its side.
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Ques:- ABOUT ME, QUALIFICATION EXPERIENCE.
Ques:- P, Q, R, S, T and U are six cities which are in a row in the same order. A bus, b1 travels from P to U and another bus b2 travel from U to P. The bus b1 reaches S at 10:40 and bus b2 reaches Q at 10:35 if the travel time between any two adjacent cities is 40 minutes and the stoppage time at each city is 15 minutes, then at what time do they start at their respective destinations?
Ques:- How would you describe your basic leadership style? Give specific examples of how you practice this?
Ques:- Manick received Rs. 6000 as his share out of the total profit of Rs. 9000 which he and Raunaq earned at the end of one year. If Manick invested Rs. 20,000 for 6 months, whereas Raunaq invested his amount for the whole year, what was the amount invested by Raunaq?
A. Rs. 3000
B. Rs. 4000
C. Rs. 5000
D. Rs. 6000
Recent Answer : Added by MANASA CHINTHALA On 2022-03-09 16:33:20:
P1/P2 = C1*T1/ C2*T2
where P1 = Partner 1’s Profit.
C1 = Partner 1’s Capital.
T1 = Time period for which Partner 1 contributed his capital.
P2 = Partner 2’s Profit.
C2 = Partner 2’s Capital.
T2 = Time period for which Partner 2 contributed his capital
6000/3000= 20,000*6/x*12
x=5000
Ques:- In an examination, 80% of the students passed in English, 85% in Mathematics and 75% in both English and Mathematics. If 40 students failed in both the subjects the total number of students is
A. 200
B. 400
C. 600
D. 800
Recent Answer : Added by Phani On 2022-03-09 16:41:44:
Percentage of people passed = (passed in eng) + (passed in math) – ( passed in both)
Which is 90% of students passed and 10% failed
10% of X = 40
X = 400
Ques:- A train 280 m long is moving at 60 km/hr. Time taken by the train to cross a tunnel 220 m long is
A. 15 sec
B. 20 sec
C. 25 sec
D. 30 sec
Recent Answer : Added by Swapna On 2022-10-07 17:19:10:
30 Sec
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Ques:- A frog in a well 30 ft deep jumps 3 ft slips 2 ft each day.How many days does take on the whole?
Recent Answer : Added by Pat On 2023-04-26 17:34:54:
Day 1: 30-3ft = 27+2ft = 29
Day 8: 23 jumps 3ft = 20 slips 2ft = 22
Day 16: 13 jumps 3ft = 10 slips 2ft = 12
Day 24: 3 jumps 3ft = Out?
Ques:- What is your strenght and weeknesess.
Ques:- Do u think u’ll be able to do job with out absence and home sick.
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.