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 a man byes 1 lt of milk for 12 Rupees and mixes with 20% of water and sells it for Rs. 15 then what is percentage of gain
Recent Answer : Added by Admin On 2020-05-17 12:00:07:
After the mixing, 1lt of the mixture has 0.8lt of milk and 0.2lt of water. 1lt of milk costs Rs.12 so 0.8lt of milk costs 0.8 x 12 = 9.6
He sells the mixture at Rs.15,
so profit%=(15-9.6)/9.6 x 100 = 56.25%
Ques:- What is the amount of pf and esi for employee to deducted ?
Ques:- The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?
Recent Answer : Added by Vipul Shukla On 2022-01-08 16:05:02:
9 years
Bcz 3×3=9
5×3=15
7×3=21
Total = 45
Avg of this 45/3 = 15
Ques:- there is number X in decimal represntation whose last digit is not 0. if digits of X are reversed then we obtain new number say Y. both X and Y are divisible by 7. then find all such X from 10 to 1000.
Recent Answer : Added by olebon On 2021-10-25 03:53:35:
77
Ques:- A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Recent Answer : Added by MAMIDI LIJITA SREE On 2023-01-21 17:36:43:
34
Ques:- About past experience and remarkable achievements. Most job satisfaction incidents.
Ques:- area of triangle=1/2*b*h base incresed by 4 times & height is devided by 2, the net effect of area.
Recent Answer : Added by Admin On 2020-05-17 12:00:14:
area is doubled.
actual area = 1/2 bh
after increase area = 1/2 *4b* h /2
=bh
1/2 *bh *2 = bh
therefore area is doubled
Ques:- What made me to rejoin siemens? relocation?
Ques:- The average weight of 25 persons sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 25 persons?
Recent Answer : Added by Admin On 2022-09-29 15:59:24:
let the average of 25 person be x
total age of a person=average×no.of person
total age of 25 person=X×25
=25X
when a new person of 46kg come average decrease by 5kg(X-5)
Total age of 26 person =25x+46
Average age of 26 person=X-5
A/Q
.25X+46=26(X-5)
25X+46=26X-130
26X-25X=130+46
X =176
hence the av. of 25 person be 176kg
Ques:- A man was employed on the promise that he will be paid the highest wages per day. The contract money to be paid was Rs. 1189. Finally he was paid only Rs. 1073. For how many days did he actually work?
Recent Answer : Added by jose On 2022-01-08 16:06:41:
23.5 days
Ques:- A ship started from port and moving with I miles per hour and another ship started from L and moving with H miles per hour. At which place these two ships meet?
Ques:- How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Recent Answer : Added by 1122 On 2022-05-17 08:56:27:
around 29.8
Ques:- Where would you like to be after five years?
Ques:- Why do you want to study MS in computer science in USA
Ques:- Find the greatest number of four digits which when divided by 10, 15, 21 and 28 leaves 4, 9, 15 and 22 as remainders respectively?
Recent Answer : Added by saikiran On 2022-08-24 17:03:44:
9654
Ques:- Product of Prime no. between 1 to 20?
Recent Answer : Added by Admin On 2020-05-17 12:02:00:
2*3*5*7*11*13*17*19=9699690
Ques:- If (n – 1) is an odd number, what are the two other odd numbers nearest to it?
A. n, n – 1
B. n, n – 2
C. n – 3, n + 1
D. n – 3, n + 5
Recent Answer : Added by Rohan On 2021-11-13 11:02:06:
c
Ques:- The banker’s discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. What is the time?
Ques:- Peter invested an amount of Rs. 12,000 at the rate of 10% p.a simple interest and another amount at the rate of 20% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested?
Recent Answer : Added by Prakash Harigopal On 2022-05-17 09:08:33:
20000
Ques:- In each questions below are given two statements followed by two conclusions numbered I and II. Statements : Some kings are queens. All queens are beautiful. Conclusions :
I. All kings are beautiful. II. All queens are kings.
A. if only conclusion I follows
B. if only conclusion II follows
C. if either conclusion I or II follows
D. if neither conclusion I nor II follows
E. if both conclusions I and II follow
Recent Answer : Added by Vayulurusurya On 2022-03-09 16:29:51:
Conclusion 1 follows
Ques:- Some boys are sitting in a row. P is sitting fourteenth from the left and Q is seventh from the right. If there are four boys between P and Q, how many boys are there in the row ?
Ques:- Give an example of something which you don’t do in a conventional way?
Recent Answer : Added by DK BOSS On 2021-07-16 09:52:46:
I am not doing my money investment in conventional manner
Ques:- Family, be thorough with ur resume
Ques:- A building contractor employs 20 male, 15 female and 5 child workers. To a male worker he pays Rs.25 per day, to a female worker Rs.20 per day and a child worker Rs.8 per day. The average wage per day paid by the contractor is?
Recent Answer : Added by amit arya On 2022-08-14 16:31:33:
21
Ques:- In a company 3/5 of people know shorthand 1/4th know typing and 1/5 know both. What fraction of people do not know both?
Recent Answer : Added by Admin On 2020-05-17 11:59:27:
4/5
Ques:- Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is:
Ques:- In country X, democratic, conservative and justice parties have fought three civil wars in twenty years. TO restore stability an agreement is reached to rotate the top offices President, Prime Minister and Army Chief among the parties so that each?
Ques:- In a class there are 20 boys and 25 girls. In how many ways can a boy and a girl be selected?
Recent Answer : Added by Rashid Ather Deshmukh On 2021-10-07 15:42:01:
500 ways
Ques:- Five farmers have 7, 9, 11, 13 & 14 apple trees, respectively in their orchards. Last year, each of them discovered that every tree in their own orchard bore exactly the same number of apples. Further, if the third farmer gives one apple to the first, and the fifth gives three to each of the second and the fourth, they would all have exactly the same number of apples. What were the yields per tree in the orchards of the third and fourth farmers?
Recent Answer : Added by John Rony On 2021-06-23 17:56:01:
So we consider the 2nd statement first. We can form an equation out of it.
14x-6=13y+3=9z+3
Using this, we can understand that the multiple of 14 and the multiple of 13 and 9 must have a difference of 9. The easiest way to ensure that is multiplying it by 9
14*9=126
13*9=117
If the 5th farmer gives 3 apples to the 4th farmer, they would have 123 and 120 apples respectively. However, we also know that the 2nd farmer has 117 apples (13*9=117, and this is a multiple of 9) if the 5th farmer gives 3 apples too the 2nd farmer, the 3rd, 4th and 5th farmers would have 120 apples each.
Now that we got 120, we should check if the first part of the question makes sense along with it. The equation would be
7a+1=11b-1=120
We know that 11*11=121 and 7*17=119. When we add 1 to 119 and subtract 1 from 121, we get 120 for each. In this way, all the farmers have 120 apples each.
Therefore, the 3rd farmer had a yield of 11 per tree and the 4th farmer had a yield of 9 per tree.
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.