Easy method for Boats and Streams

Today i am going to discuss about Boats and streams problems. Observe the below image and note down in your paper as 3 different pictures. Then those are enough to answer any type of BOATS AND STREAMS problem. So, lets see how it works. First of all, see those three vertical broad lines. They denotes Up stream, Speed in still water, and Down stream. And the two small ones are both same, they are stream speeds. When you want to solve this boats problem, draw these lines and mention their appropriate numbers, given in the problem.

Now, we will take an example problem, to solve.

A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.

 

now, we will take another example to solve in this method.

In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Sol : You can see the difference between up(against) and Down (along or with)is 11-5 =6
as we have 2 stream speed lines, 6/2 = 3kmph is the stream speed.
now, subtract 3 from 11 or add 3 to 5 which implies 8 anyways.
hence still water speed is 8kmph.

This may take a while to remember. But with this it is easy to minimize time in our examinations.

NOTE : Here is a note to mention. When the arrow going to down stream, it is a plus. ie you need to add when it is down arrow. And Up arrow.. minus

 If you may find difficult to remember plus or minus sequence, one small hint is there. Always up stream is lesser than down stream. UP < DOWN

Here i am giving you some problems. Try solving it out.


1. A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. What is the speed of the stream (in km/hr)

2. A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is?

3. A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?

4. A boat covers a certain distance downstream in 1 hour, while it comes back in 1 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?

5. 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?

6. A man can row at 5 kmph 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?

7. The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance traveled downstream in 12 minutes is?



Hope this is useful to you and understood. If there is any doubts, pls find time to post me. I'll try my best to answer you. And also if you find any mistakes, make a note of it too. :) see you

Solved Numerical Aptitude Questions

Question 1: The sum of the ages of husband and wife is 70 years and the ratio of their age is 3 : 2. The age of the wife is:

1. 32 years 
2. 25 years

3. 28 years

4. 27 years
5.

Correct Answer: 3.


Question 2: A trader would incur a loss of 15%, if he sells pens at 10.20 per pen. If 12.5% profit is to be earned after allowing 10% discount on the marked price then find the marked price. ?

1. 20
2. 1.5
3. 150
4. 12
5. 15

Correct Answer: 5.


Question 3: A shopkeeper sells sugar at 4% less than market price, but gives weight 800 grams instead of 1 Kg. What is the profit percentage overall?

1. 5%
2. 10%
3. 20%
4. 25%
5. 12%

Correct Answer: 3.


Question 4: What is the location of the atomic power station?

1. Mumbai
2. Tarapore
3. Kalpakkam
4. Kaiga
5.

Correct Answer: 2.


Question 5: A shirt was sold at a profit of Rs.50. If a trouser was sold at half the profit percenta9e and the cost price of the trouser is thrice that of the shirt, find the profit made on the trouser (in Rs.)

1. 25
2. 57
3. 75
4. 50
5.

Correct Answer: 3.


Question 6: The average runs scored by a batsman in 20 matches is 40. In the next 10 matches, the batsman scored an average of 13 runs. Find his average in all the 30 matches.

1. 27
2. 26
3. 31
4. 29
5.

Correct Answer: 3.


Question 7: 729 ml of a mixture contains milk and water in ratio 7 : 2. How much more water is required to be added to get a new mixture containing milk and water in the ratio of 7 : 3?

1. 60 ml
2. 70 ml
3. 81 ml
4. 90 ml
5.

Correct Answer: 3.


Question 8: What is the difference between the simple interest and the compound interest on a sum of 4700 at 20% p.a. for a period of 2 years ?

1. Rs.190
2. Rs.188
3. Rs.196
4. Rs.199
5.

Correct Answer: 2.


Question 9: If a trader sold two cars each at 325475 and gains 12% on the first and loses 12% on the second, then his profit or loss percent on the whole is?

1. 14.48% loss
2. 14.4% loss
3. 14.4% profit
4. 1.44% loss
5.

Correct Answer: 2.


Question 10: A trader wants to sell a watch at 25% profit. If its cost price was Rs.x more, an extra profit of 50.would be made on it. Find x (in Rs.)

1. 100
2. 125
3. 130
4. 145
5. 200

Correct Answer: 5.


Question 11: In how many years does a sum of Rs.5000 give a simple interest of Rs.16500 at 15°, p.a.?

1. 22
2. 24
3. 25
4. 23
5.

Correct Answer: 1.


Question 12: A certain sum becomes Rs.20720 in 4 years and 24080 in 6 years at simple interest. Find sum and rate of interest.

1. Rs.12000; 12% p.a
2. Rs.14000; 12% p.a
3. Rs.12000; 15% p.a
4. Rs.14000; 15% p.a
5.

Correct Answer: 2.


Question 13: Francis and George started a business with investments of Rs.7000/- and Rs.10000/-. After x months, Francis left. After two more months David joined the business with an investment of Rs.10000/-. If the annual profit is shared among David, Francis and George in the ratio 10 : 7 : 24, find the respective time periods of David, Francis and George for which they stayed that year.

1. 5:5:12
2. 1:1:3
3. 1:1:4
4. 1:1:2
5.

Correct Answer: 3.


Question 14: 89.447+98.3+67.77=_____________

1. 254.417
2. 250.146
3. 254.369
4. 2549369
5. 255..517

Correct Answer: 5.


Question 15: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining is 90. Find the number of students who wrote the exam.

1. 15
2. 20
3. 25
4. 35
5.

Correct Answer: 3.


Question 16: The difference between 38% of number and 24% of the same number is 135.10. what is 40% of that number ?

1. 394
2. 370
3. 378
4. 386
5. None of these

Correct Answer: 4.


Question 17: 29.299+5.55+68.7=____________________________

1. 104.236
2. 123.569
3. 103.549
4. 124.263
5. 25.25521

Correct Answer: 3.


Question 18: A and B can do a work in 20 and 30 days respectively. They started the work together, but A left after some time and B finished the remaining work in 5 days. Then what is the number of days after which A left?

1. 5
2. 10
3. 12
4. 15
5. None of these

Correct Answer: 2.


Question 19: Avinash purchases five cycles at the rate of Rs 450 per cycle. He spends Rs 150 on each cycle for repairs. At what price he should sell them to gain a profit of 35%?

1. Rs 600
2. Rs 750
3. Rs 608
4. Rs 810
5.

Correct Answer: 4.


Question 20: A sold an article to B at 10% profit and B sold it to C at 15% profit. If B purchased for Rs.220/-, then find the difference in the purchasing prices for A and C.

1. 35
2. 53
3. 45
4. 78
5.

Correct Answer: 2.


Question 21: A shopkeeper sold an Air-conditioner for Rs 25,935 with a discount of 9% and earned a profit of 3.74%. What would have been the percentage of profit earned if no discount were offered?

1. 15.6%
2. 16% 
3. 12.3%
4. None of the above
5.

Correct Answer: 4.


Question 22: Two equal glasses are respectively 1/4 and 3/4 full of milk. They are then filled up with water and the contents are mixed in a tumbler. The ratio of milk and water in the tumbler is:

1. 3 : 11
2. 7 : 17
3. 9 : 23
4. 11 : 23
5.

Correct Answer: 2.


Question 23: Pick the odd number from the series - 11, 12, 8, 27, 10.75, 56.5

1. 12
2. 8
3. 27
4. 10.75
5. 56.5

Correct Answer: 5.


Question 24: 9.75 + 25.88 + ? = 41.18

1. 5.55
2. 5.75
3. 6.57
4. 4.23
5.

Correct Answer: 1.


Question 25: The value of a machinery decreases by 20% p.a. on the value at the beginning of every year. The value of the machinery after 2 years will be Rs.23526,40. What is the present value of the machinery?

1. Rs.36770
2. Rs.36750
3. Rs.36740
4. Rs.36760
5.

Correct Answer: 2.

RATIO AND PROPORTION

RATIO

  Ratio means the number of times one quantity contains another quantity of the same kind. The comparison is made by considering what part or multiple the first quantity of the second.
       Thus the ratio between Rs 50 and Rs 200 can be possible, but not between Rs 50 and 200 marks.
       The ratio between one quantity to another is measured by  a : b or a/b
^{Ex: 8:9   or   5:7 etc.
       The two quantities in the ratio are called its terms. The first is called the antecedent and the second term is called consequent.}
 

^{Types of Ratios:}
 

^{1. Duplicate ratio: The ratio of the squares of the two numbers.
     Ex: 9 : 16 is the duplicate ratio of 3 : 4.}
 

^{2. Triplicate Ratio: The ratio of the cubes of the two numbers.
     Ex: 27 : 64 is the triplicate ratio of 3 : 4.}

<sup>3. Sub-duplicate Ratio: The ratio between the square roots of the two numbers.
      Ex: 4 : 5 is the sub-duplicate ratio of 16 : 25.
 
4. Sub-triplicate Ratio: The ratio between the cube roots of the two numbers.
      Ex: 4 : 5 is the sub-triplicate ratio of 64 : 125.
 
5.Inverse ratio: If the two terms in the ratio interchange their places, then the new ratio is inverse ratio of the first.
      Ex: 9 :5 is the inverse ratio of 5 : 9.
 
6. Compound ratio: The ratio of the product of the first terms to that of the second terms of two or more ratios.
      Ex: The compound ratio of</sup>  3/4, 5/7, 4/5, 4/5 is 9/35
 



^{PROPORTION 
If two ratios are equal, then they make a proportion.
 Thus}  4/5 = 8/10 or 4:5 = 8:10
^{Each term of the ratios 4/5 and 8/10  is called proportional.
The middle terms 5 and 8 are called means and the end terms 4 and 10 are called extremes.}

Product of Means = Product of Extremes

^{Continued Proportion: In the proportion  8/12= 12/8  8, 12, 18 are in the continued proportion.}
 

^{Fourth proportion: If a : b = c : x, then x is called fourth proportion of a,b and  c.
There fore fourth proportion of  a, b, c  =} b x c/a
 

^{Third proportion: If a : b = b : x, then x is called third proportion of a and b.
Therefore third proportion of a, b =  b^2/a}
 

^{Second or mean proportion: If a : x = x : b , then x is called second or mean proportion of a and b.
Therefore mean proportion of a and b =  root(ab)}

EXAMPLES

^{Example 1: Find out the two quantities whose difference is 30 and the ratio between them is 5/11.
Sol: The difference of quantities, which are in the ratio 5:11, is 6. To make the difference 30, we should Multiply them by 5.
        Therefore  5:11 = 5x5 : 11x5 = 25 : 55}
 

^{Example 2: A factory employs skilled workers, unskilled workers and clerks in the ratio 8:5:1 and the wages of a skilled worker, an unskilled worker and a clerk are in the ratio 5:2:3 when 20 unskilled workers are employed the total daily wages fall amount to Rs. 318. Find out the daily wages paid to each category of employees.
Sol: Number of skilled worker: unskilled worker: clerks = 8:5:1 and the ratio of their respective Wages = 5:2:3
       Hence the amount will be paid in the ratio 8 × 5 : 5 × 2 : 3 × 1 = 40 : 10:3          
       Hence total amount distributed among unskilled workers
                                   318  x 10 / (40+10 +3)} = Rs 60.

^{But the number of unskilled workers is 20, so the daily wages of unskilled worker
                                                      60/20 = rs.30
The wages of a skilled worker, an unskilled worker and a clerk are in the ratio = 5:2:3
      Multiplying the ratio by (5/2) and (3/2)we get = 7.50 : 3 : 4.50
      So, if an unskilled worker gets Rs.3 a day then a skilled worker gets Rs. 7.50 per day a clerks Rs. 4.50 a day
 
Example 3: Two numbers are in the ratio of 11:13. If 12 be subtracted from each, the remainders are in the ratio of 7:9 Find out the numbers.
Sol: Since the numbers are in the ratio of 11:13. Let the numbers be 11x and 13x. Now if 2 is subtracted from each, the numbers become (11x -12) and (13x-12).  As they are in the ratio of 7:9              (11x-12): (13x-12):: 7: 9
                (11x – 12) 9 = (13x – 12) 7
                99x – 108 = 91x – 84
                9x = 24 or x = 3
  Therefore the numbers are 11 x 3 = 33 and 13 x 3 = 39}

Example 4:  In what ratio the two kinds of tea must be mixed together one at Rs. 48 per kg. and another at Rs. 32 per kg. So that the mixture may cost Rs. 36 per kg. ? Sol:  Ratio of inferior quality to superior quality=(rate of superior - rate of mix)/(rate of mix- rate of inferior) = (48-36)/(36-32) =12/4 =3:1

^{Example 5:  If Rs. 279 were distributed among Ram, Mohan and Sohan in the ratio of 15:10:6 respectively, then how many rupees did Mohan obtain?
Sol: Ratio in which Ram, Mohan and Sohan got  = 15 :10 : 6
                        Sum of ratios  = 15 + 10 + 6 = 31
                        Share of Mohan} = (10 x 279)/ 31
                                                         ^{= Rs. 90
 
Example 6:  A bag contains of one rupee, 50 paise and 25 paise coins. If these coins are in the ratio of 2:3:10, and the total amount of coins is Rs288, find the number of 25 paise coins in the bag.
Sol:   Ratio of one rupee, 50 paise and 25 paise coins
                                                                 = 2:3:10
                        Ratio of their values  = 8:6:10 = 4:3:5
 And sum of the ratios of their values = 4 + 3 + 5 = 12
                     Value of 25 paise coins (5x288)/12 = Rs. 120
                      No. of 25 paise coins   = 120 × 4 = 480}