Boat and Stream-Boat and stream question and answer

Boat and Stream

Knowing the entire exam syllabus and all relevant themes is crucial for any competitive exam candidate who wants to advance in his or her career in the government sector and private sectors .we discussed about Boat and Stream:

Stream and Boat idea:

Answering queries supported the boat and stream notion involves variety of subconcepts. The four terms that a candidate must comprehend so as to understand the notion of streams area unit listed below.

Stream: -A river's flowing water is cited as a stream.

Upstream :- a ship is claimed to be moving upstream if it's moving downstream of the stream. The boat's upstream speed during this state of affairs is its web speed.

Downstream: - a ship is claimed to be moving downstream if it's occupation a similar direction because the stream. during this instance, the boat's downstream speed is its web speed.

Still Water: - during this case, the water is seen as being immobile.

 

Formula for  Boat and Stream:- 

Upstream:- (u−v) km/hr

Downstream:- (u+v)Km/hr

Speed of Boat in Still Wate:-r ½ (Downstream Speed + Upstream Speed)

Speed of Stream :-½ (Downstream Speed – Upstream Speed)

Average Speed of Boat:- {(Upstream Speed × Downstream Speed) / Boat’s Speed in Still Water}

Speed of boat or swimmer in still water:- 1/2 (Downstream Speed + Upstream Speed)

Example of Boat stream questions :

Q. If the ratio of the speed of a boat in upstream and the speed of the stream is 8 : 1. If

the boat can travel 500 km downstream in 20 hours then find the total distance

travelled by the boat in still water in the same time?

A. 425 km

 B. 459 km

 C. 441 km

 D. 450 km 

E. None of these

Q.In downstream, two steamers A and B start simultaneously from the point P but the

steamer B reaches point Q, 2 hours before the steamer A reaches the same point. If

the distance between point P and Q is 120 km and the speed of steamer B in upstream

is 3 km per hour more than that of steamer B in upstream and the speed of stream is 2

km per hour, then find the sum of the speed of steamer A in still water and that of

steamer B in still water?

A. 21 km per hour

 B. 20 km per hour

 C. 23 km per hour 

D. 27 km per hour

 E. None of these

Q.The distance between two points on a river is D km. A man rowing a boat along the

stream finds that the distance of rowing along the stream is 30 times the total

distance and when he started rowing against the stream the distance he rowed was

found 4 times of total distance. The total time taken against the stream is 10% more

than that along the stream. If the boat cover 135 km along the stream in 9 hours.

What is the speed of stream?

A. 3 km/h 

B. 3.25 km/h 

C. 3.5 km/h

 D. 2.5 km/h

 E. None of these

Q..A motorboat, whose speed in 20 km/hr in still water goes 40 km downstream and comes back in a total of 5 hours . The speed of the stream (in km/hr) is: A. 13 km/h  B. 25 km/h  C. 35 km/h  D. 20 km/h  E. None of these

Q. In one hour, a boat goes 15 km/hr along the stream and 7 km/hr against the stream. The speed of the boat in still water (in km/hr) is:

 A. 12 km/h 

B. 10 km/h 

C. 11 km/h

 D. 09 km/h

 E. None of these

Q. A man's speed with the current is 18 km/hr and the speed of the current is 3.5 km/hr. The man's speed against the current is:

 A. 12 km/h 

B. 10 km/h 

C. 11 km/h

 D. 09 km/h

 E. None of these

Q. The speed of a boat in still water in 20 km/hr and the rate of current is 4 km/hr. The distance travelled downstream in 20 minutes is:

 A. 8 km/h 

B. 5 km/h 

C. 10 km/h

 D. 9 km/h

 E. None of these

Profit and loss In Mathematic

 

Profit and loss in mathematics

In mathematics, the price of a product on the market and an organization’s profitability are determined using the profit and loss formula. For every good, there is a selling price and a cost price. Based on the values of these prices, we can determine the profit or loss for a certain product. 

This article's main topics(Profit and loss in mathematics) include cost price, fixed, variable, and semi-variable costs, selling price, marked price, list price, margin, etc.Here, we also learn about the formula for profit and loss percentages. For instance, if a dealer’s selling price is higher than the product’s cost price, they are making a profit; if the cost price is higher than the selling price, they are losing money. 

Formula of  Profit and loss 

👉 C.P. = Cost Price (Purchasing Price + Repairing/ Maintenance Cost, {if any})

👉 S.P =  Selling Price

RULES :- 

Successive Profits :- If A sells an article to B at a% profit and B sells it to C at b% profit OR If a% and b% are two successive profits 

👉 Then , Total Profit% = {a +b+(ab/100)}%

✅ If A sells an article to B at a% profit and B sells it to C at b% profit and if C paid x .

👉 Then , The amount paid by A = X ✖{100/(100+a)}{100/(100+b)}

Successive losses :-: If a% and b% are two successive losses  (negative sign shows loss and positive sign shows profit). 

👉 Then , Total loss% ={ -a -b+(ab/100)}%

☑ If a% profit and b% loss occur, simultaneously . 

👉 Then , overall loss or profit% is = {a -b-(ab/100)}% 

✔NOTE :- (-ve sign for loss, +ve sign for profit)

☑  If a% loss and b% profit occur .

👉 Then , overall loss or profit% is = { -a +b-(ab/100)}% 

Example :-

1. Rahul sell a Fan to Rahim with 10% profit and Rahim sell the Fan to Raju with 5% profit calculate the total profit ?

(a) 14.5% (b) 15.5 % (c) 16.5% (d) 17.5%

Answer :- (b) 15.5 % [Formula:- {a +b+(ab/100)}%]

2. Raj sell a  Bag to Nabita with 12% profit  and Nabita sell the Bag to Riju with 10% profit . calculate the total profit ?

(a) 21.2% (b) 22.2% (c) 23.2% (d) 24.2%

Answer :- (c) 23.2% [Formula :- {a +b+(ab/100)}%]

3. Rita sell a  watch  to Rubi with 5% profit and Rubi sell the watch to Puja with 7% profit and right now 220 . What amount paid by Rita for buy ?

(a)195.82 (b)200 (c)193.80 (d)202

Answer :-(a)195.82 [Formula :-X ✖{100/(100+a)}{100/(100+b)}]

Time and work -Time and work in mathematics

👉 Time and work👈

Aspirants who will be taking competitive examinations for the first time or who have been preparing for the exams for some time should be aware that each subject has to receive enough time so that the concepts and fundamentals are understood. You will be better able to handle the challenging competition for each exam.We explain the concepts of time and work in this post, along with formulas that will make it easier for you to respond to inquiries. Additionally, we have a few sample time and work problems with solutions farther down in the post for your reference.

The following links will help interested candidates improve their preparation for the quantitative aptitude test.

One thing to keep in mind is that every task required a specific amount of time.

Efficiency multiply time taken equals work completed.

It means

Work completed= efficiency  x  time taken.

Basic formula for work and time:-

Rule 1: Start with days:

If a person can do a task in n days (or hours), then the task takes that individual 1/n days (or hours).

Rule 2: Days from work:

If a person's work in 1 day (or hour) equals 1/n, they will finish the task in n days (hours).

Rule - 3

If one individual is n times more productive than another, then the work done by:

First-person work to second-person work ratio is n: 1.

Ratio of times taken by First person and second person to finish a work = 1 : n.

Rule - 4

If ratio of numbers of men required to complete a work is m : n, then the ratio of time taken by them will be n : m.

Example of time and work:-

1. A can complete a task in 15 days while B needs 20. The amount of work remaining after four days of collaborative effort is:

Ans:-8/15.

2. While B can complete the same task in 12 days, A can lay railroad track between two given stations in 16 days. They completed the task in just 4 days with C's assistance. C alone can then complete the task in:

Ans:-48/5.

3. In 20, 30, and 60 days, respectively, A, B, and C can complete a task. If B and C help A every third day, how many days would it take him to complete the task?

Ans:-15 days.

4.A is thrice as economical as B and is, therefore, able to end a chunk of labor ten days prior to B. In what number days A and B can end it together?

Answer: . 5 days

Explanation: WC = 3:1

WT = 1:3

x ------- 3x

1/x – 1/3x = 1/10

x = 20/3

3/20 + 1/20 = 1/5 => five days

5.A work that may well be finished in nine days was finished three days earlier once ten additional men joined. the amount of men utilized was?s

Answer: .20 men

Pipes And Cisterns in Mathematics

 Pipes & Cisterns  in Mathematics 

This article will introduce you to the idea of pipes and cisterns as they are presented in competitive exams, as well as the kind of questions that may be given, some key formulas for answering them, and a few practise problems to help you grasp the subject better.
Candidates who intend to apply for the upcoming government sector exams should begin preparing right away because the competition is fierce and the exams are challenging to pass.
The following links provide further information on the other quantitative aptitude concepts covered in the Government exam segment for interested candidates:

✅ Basic:- Problems on Pipes and Cisterns are based on the basic concept of time and work. Pipes are connected to a tank or cistern and are used to fill or empty the tank or cistern. In pipe and cistern, the work is done in form of filling or emptying a cistern/tank.

👉Types Of Pipes :-

 ☑   Inlet pipe It fills a tank/cistern/reservoir. 

 ☑   Outlet pipe It empties a tank/cistern/reservoir.

✅Note :-  

  

 👉 If a pipe cab fill/empty a tank in 'm' h , then the part of  tank filled /emptied in 1h = 1/m . 

 

 ☑ Example : A pipe can fill/empty '1/m' part of a tank in 1 h, then the volume of tank filled in 1 h = 1/7

 👉 If a pipe can fill /empty '1/m' part of a tank in 7 h then  it can fill/empty the whole tank in 'm' h.

☑ Example : If a pipe can fill 1/5 part of a tank in 1 h then it can fill the whole tank in 5h .

👉Generally , time taken to fill a tank is taken positive (+ve) and time taken to empty a tank is taken negative (-ve). 

👉 If a pipe fills a tank in 'm' 'h' and an another pipe fills in 'n' 'h' . Then , part filled by both pipes in 1 h = 1/m +1/n.

✅Example Of The Math

👉 1. An outlet pipe can empty a cistern in 5h , In what time will the pipe empty 2/5 part of the cistern ?

✔Answer:-  Time taken to empty full cistern = 5h

                     Time taken to empty 2/5 part of the cistern = 2/5 *5 = 2h 

👉 2 If a pipe can fill a tank in 2 h and another pipe can fill the same tank in 6 h, then what part of a tank will be filled by both the pipes in 1 h, if they are opened simultaneously? 

✔Answer:-  In 1h , part filled by 1st pipe = 1/m = 1/2

                    In 1h part filled by 2nd pipe = 1/n = 1/6

                   .'. In 1h , part filled by both the pipes together = (1/m+1/n)

                                                                                                   = (1/2+1/6)

                                                                                                   = (3+1)/6 = 4/6 =2/3 part ✔ 

👉3 When opened separately, the two pipelines P and Q may fill the tank in 20 and 30 hours, respectively. How long would it take to fill the tank if both lines are opened at once?

Answer 

Pipe fills a portion of the tank. P = 1/20 in 1 hour. Pipe Q filled 1/30 of the tank in an hour.

Tank filled in 1 hour by both pipes: 1/20 + 1/30 = 5/60 = 1/12

Both will fill the tank to capacity in 12 hours.

Pipe A can fill a tank in 5 hours, while Pipe B can empty it in 8 hours, respectively. How long will it take the tank to fill halfway?

Profit and loss in mathematics

Profit and loss in mathematics

In mathematics, the price of a product on the market and an organization’s profitability are determined using the profit and loss formula. For every good, there is a selling price and a cost price. Based on the values of these prices, we can determine the profit or loss for a certain product. 

This article's main topics(Profit and loss in mathematics) include cost price, fixed, variable, and semi-variable costs, selling price, marked price, list price, margin, etc.Here, we also learn about the formula for profit and loss percentages. For instance, if a dealer’s selling price is higher than the product’s cost price, they are making a profit; if the cost price is higher than the selling price, they are losing money.

Formula of  Profit and loss 

👉 C.P. = Cost Price (Purchasing Price + Repairing/ Maintenance Cost, {if any})

👉 S.P =  Selling Price

  RULE 1 : If S.P > C.P. then there will be profit . And the profit will be calculate as = S.P - C.P . 

☑ Profit% = (100✖ Profit)/ Cost Price 

 RULE 2 : If C.P > S.P., then there will be Loss . And loss will be calculate as = C.P - S.P

☑ Loss% = (100✖ Loss)/ Cost Price 

RULE 3 : If an object is sold on x% Profit

👉 Then , S.P = C.P{(100+Profit%) / 100} & C.P = S.P{100 / (100+Profit%)}

✅ If an object is sold on x% loss

👉 Then , S.P = C.P{(100 - Loss%) / 100} & C.P = S.P{100 / (100 - Loss%)}

S.P. = 100 100 L - N M O Q P Loss% or C.P. = S.P. 100 100- L N M O Q P Loss% 

Profit and Loss Tricks:-

Profit, P = SP – CP; SP>CP
Loss, L = CP – SP; CP>SP
P% = (P/CP) x 100
L% = (L/CP) x 100
SP = {(100 + P%)/100} x CP
SP = {(100 – L%)/100} x CP
CP = {100/(100 + P%)} x SP
CP = {100/(100 – L%)} x SP
Discount = MP – SP
SP = MP -Discount

 Example:-

1. A man buys a cycle for 1200 and sells it at a loss of 5%. What is the selling price of the cycle?

  (a) 1202 (b) 1190 (c) 1160 (d) 1140

Answer:-  (d) 1140

2. On selling an article for 657, there is a loss of 10%. The cost price of that article is

 (a) 744 (b) 751 (c) 730 (d) 700

Answer :- (c) 730

3. A milkman bought 80 liters of milk for 720 and added 10 liters of water. If he sells it at 9.00 per liter, his profit percentage is

 (a) 8.15 % (b) 7% (c) 8.25 % (d) 12.5%

Answer :- (d) 12.5%

Understand Of Ratio

   

About Ratio 

  What Is Ratio ?

 👉The Ratio is the when two or more quantity are compared, in this time we can determine the comparison between the quantity's . 

 👉The ratio between A and B can be represented as A : B , where A is called antecedent and B is called consequent 

 ☑ Example :-  For example There can be a ratio between  200 and  400, but there cannot be the ratio between  200 and 400 apples. Hence, the units of quantity for the comparison of ratio should  be same.

                         👉 Ratio should be 200 : 400 = 1:2

 

Types of Ratio : - 

 ➤  Duplicate Ratio : - In this ratio for select that  X is one quantity and another is  Y then the quantity 's squares ratio also same that type ratio is called Duplicate Ratio 

 ☑ Example : the ratio of number 3 and 4 is = 3 : 4 and also squares of the 3 and 4 's ratio is 9:16 that means 3:4 = 9:16 like that X r :Yr 

➤ Sub-duplicate Ratio :-  If two numbers are in ratio, then the ratio of their square roots are  called sub-duplicate ratio. If x and y are two numbers, then the sub-duplicate ratio of x and y would be Vx : Jy.

☑ Example : the ratio of number 3 and 5 is = 3 : 5 and also squares of the 3 and 5 's ratio is 9:25 like that Vx : Jy. 

➤  Triplicate Ratio  If two numbers are in ratio, then the ratio of their cubes is called triplicate ratio. If x and y are two numbers, then the triplicate ratio of x and y would be x^y3 . 

 

 ☑ Example :Triplicate ratio of 2 :3 = 2^3 :3^3 = 8 :27

➤  Sub-triplicate Ratio:- If two numbers are in ratio, then the ratio of their cube roots is called sub-triplicate ratio. If x and y are two numbers, then the sub-triplicate ratio of x and y would be 3/x : ^/y.

  ☑ Example :  Sub-triplicate ratio of 1:125 = 3/1 : 3/125 =1:5 

➤  Inverse Ratio:-  If two numbers are in ratio, then their antecedent and consequent are interchanged and the ratio obtained is called inverse ratio, If X and Y are two numbers and their ratio is X : Y, then its inverse ratio will be Y : X. 

 ☑ Example : Inverse ratio of 4 :5 is 5 :4 . 

➤   Compound Ratio:- If two or more ratios are given, then the antecedent of one is multiplied with antecedent of other and respective consequents are also multiplied. If a : b, c: d and e : / are three ratios, then their compound ratio will be ace: bdf . 

☑ Example : The ratio are 3:5 , 4:7 , 5:7 for the compound Ratio is 

                        (3*4*5)/(5*7*7) = 12/49= 12:49

✅Note   

  ✔✔ If the antecedent is greater than the consequent, then the ratio is known as the ratio of greater inequality, such as 7 : 5 .

 ✔✔ If the antecedent is less than the consequent, then the ratio is called the ratio of less inequality, such as 5 : 7 . 

   Short tricks of LCM

In  previous post we discuss about what is LCM

, who invented LCM in details

Short tricks of LCM 

Now a days there are  many short tricks  available in the internet so  we  discuss the major tricks to solve the LCM  Problem

Trick 1:-

If  all the   is divicible  to the  greatest number

The the LCM is  the greatest number. 

Eg:-

3,6,12,24

Ans :-24

Trick 2:-

If  there  are  4 number  are given  , the greatest number is divicible   two number  then you check  the undivicible number is prime number Or not if  prime  number the simply multiple the 

Greatest and prime number   this multiplication is LCM eg :- the greatest number is 10 and prime number is 7  then 10 x 7=70  is LCM

 Example:-

Q ➤ Find LCM OF 6 , 12,24,3Ans ➤ 24

Q ➤ Find LCM of 5,10,30,20Ans ➤ 60

Q ➤ Find the LCM of 2,4,8,16Ans ➤ 16

Q ➤ Find the LCM of 2,4,7,8Ans ➤ 56