In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and chose the correct option. Quantity A: The ratio of speed of boat to speed of stream is 2 : 1, If the boat travels 162 km and come back to starting point in 36 hour. What is the difference between the time taken by the boat to go upstream and the time taken by the boat to go downstream Quantity B: The speed of the stream is 6 km/hr and the distance travelled by the boat is 60 km. If the boat covered half distance upstream with usual speed and other half with double its speed, then it takes 7.5 hours less time than usual time to go upstream. Find the total time taken by the boat to go upstream and downstream?

LohaHridoy
  1. Quantity A > Quantity B
  2. Quantity A < Quantity B
  3. Quantity A = Quantity B
  4. Quantity A ≤ Quantity B
  5. Quantity A ≥ Quantity B

0 like 0 dislike
1 views
Share with your friends

1 Answers

AhmedNazir

Call

Option 2 : Quantity A < Quantity B

Quantity A:

Ratio of speed of boat to speed of stream = 2 : 1

Let Speed of Boat, SB = 2a and Speed of Stream, SS = a

TU + TD = Total time taken

⇒ Distance/ (Speed of boat downstream) + Distance/ (Speed of boat upstream) = Total Time taken

⇒ 162/ (2a + a) + 162/ (2a - a) = 36

⇒ 162 × = 36

⇒ (2a - a + 2a + a)/((2a + a) × (2a - a)) = 36/162

⇒ 4a/3a² = 2/9

⇒ 36a = 2 × 3a²

⇒ a = 6 km/hr

SS = 6 km/hr and SB 12 km/hr

Difference in time = 162/(12 - 6) - 162/(12 + 6) = 27 - 9 = 18 hours

Quantity B:

Let Speed of boat, SB = a km/hr

T - (TD + TU) = 7.5

⇒ 60/(a - 6) - 30/(a - 6) - 30/(2a - 6) = 7.5

⇒ 30/(a - 6) - 30/(2a - 6) = 7.5

⇒ 30 = 7.5

⇒ (2a - 6 - a + 6)/((a - 6)(2a - 6)) = 7.5/30

⇒ a/((a - 6)(2a - 6)) = 1/4

⇒ (a - 6)(2a - 6) = 4a

⇒ 2a² - 6a - 12a + 36 = 4a

⇒ 2a² - 22a + 36 = 0

⇒ a² - 11a + 18 = 0

⇒ a² - 2a - 9a + 18 = 0

⇒ a(a - 2) - 9(a - 2) = 0

⇒ (a - 2)(a - 9) = 0

⇒ a = 9 km/hr and 2 km/hr

Speed of boat is always greater than the speed of stream so, SB = 9 km/hr

Total time taken = 60/(9 + 6) + 60/(9 - 6) = 4 + 20 = 24 hours

∴ Quantity A < Quantity B

0 like 0 dislike
1 views
Talk Doctor Online in Bissoy App
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: A man started his journey at a speed of 54 km/hr. and covered a distance of 135 km. At what speed should he travel to complete his total journey of 360 km in 7 hours Quantity B: A bus covered a distance of 160 km in 2.5 hours and 120 km in 2.5 hours. What is its average speed?

Option 2 : Quantity A < Quantity BSolving for Quantity A: Time taken to cover 135 km = Distance/Speed = 135/54 = 2.5 hours Remaining distance to travel = 360 – 135...

1 Answers 1 views
A man starts from point ‘O’, travels 20 km towards east to reach point ‘A’, turns right and travels 10 km to reach point ‘B', turns right and travels 9 km to reach point ‘C’, turns right and travels 5 km to reach point ‘D’, turns left and travels 12 km to reach point ‘E’ and then turns right and travels 6 km to reach point ‘F. What is the shortest distance between point ‘E’ and point ‘C’?

Option 1 : 13[ alt="31-Aug Shift 3 Shivraj 21Q Rashi hindi reviewed images Q21" src="//storage.googleapis.com/tb-img/production/19/04/31-Aug_Shift%203_Shivraj_21Q_Rashi_hindi_reviewed_images_Q21.PNG"> To calculate shortest distance between E and C, (EC)2 = (ED)2 + (DC)2 = (12)2 + (5)2...

1 Answers 1 views
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for both the quantities and choose the correct option. Quantity A: A train completes its journey of 500 km running equal distance at speeds of 60 km/hr. and 90 km/hr. What is the average speed of the train in its journey Quantity B: 81?

Option 2 : Quantity A < Quantity BQuantity A: When a moving body is running at two different speeds of ‘x’ km/hr. and ‘y’ km/hr., then its average speed is computed...

1 Answers 1 views
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: A 160 m long train crosses a 200 m long platform in 18 seconds. What is the speed of the train Quantity B: A train completes its journey of 500 km running equal distance at speeds of 60 km/hr. and 90 km/hr. What is the average speed of the train in its journey?

Option 5 : Quantity A = Quantity BSolving for Quantity A: Time taken to cross the platform = Sum of the lengths of train and platform/Speed of train ⇒ Speed of train =...

1 Answers 1 views
Given below are two quantities named A and B. Based on the information, you have to determine the relationship between two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A∶ Total time taken by a boat travelling from A to B and B to A, is 1 hr 4 min. Speed of the boat in still water is 16 km/hr and speed of the current is 4 km/hr. what is distance between A to B Quantity B∶ Total time taken by a boat travelling from A to B and B to A, is 1 hr 10 min. speed of the boat in still water is 18 km/hr and speed of the current is 2 km/hr. what is distance between A to B?

Option 2 : Quantity A < Quantity BSolving for Quantity A: Speed of boat in still water = 16 km/hr Speed of the current = 4 km/hr Speed upstream = (16 - 4) =...

1 Answers 1 views
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for both quantities and chose the correct option. Quantity A: A man takes 11/9 times downstream time to row upstream keeping the distance same in both cases. What is the speed of boat (m/s) in still water if it takes 6 hours to travel 80 km in downstream Quantity B: A boat running in upstream covers 20 km distance in 3 hours while covering the same distance in downstream it takes 2 hours. What is the speed of the boat in still water (m/s)?

Option 1 : Quantity A > Quantity BSolving for Quantity A - Distance cover = 80 km Time taken = 6 hours Speed of downstream = 80/6 = 13.33 kmph Speed of downstream =...

1 Answers 1 views
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and chose the correct option. Quantity A: Height of cylindrical jar is increased by 44%. By what percent must the radius be decreased so that there is no change in volume Quantity B: Diameter of cylindrical jar is increased by 21%. By what percent the height must be decreased so that there is no change in volume?

Option 2 : Quantity A < Quantity BSolving for Quantity A: Volume of the cylindrical jar = πr2h Where, r = radius of the cylinder, h = height of cylinder Increased in the height...

1 Answers 1 views
The following question, there are three statements I, II and III. Read the question carefully and mark your answer according to which statements(s) is/are sufficient to the answer the question. What is the Speed of the stream Statement I: The distance between two points A and B is a km and the boat cover 90km along the stream in 5 hours. Statement II: The distance travelled along the stream is four times the total distance and that against the stream is three times the total distance Statement III: The total time taken against the stream is 10% more than that along the stream?

Option 3 : All I, II and IIILet x be the speed of the boat and y be the speed of the steam From statement I, ⇒ = 5 ⇒ (x + y)...

1 Answers 1 views
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and chose the correct option. Quantity A: Simple interest on certain money at a certain annual rate of interest is 25/64 of the money. If the time and rate are equal in number then, find the rate of interest Quantity B: At what rate of interest Rs. 6000 must be given at simple interest for 6 months to earn Rs. 150?

Option 1 : Quantity A > Quantity BQuantity A: Time = Rate (Given) S.I. = (P × R × T) /100 ⇒ 25x/64 = (64x × R × R)/100 ⇒ R2 = 2500/64 ⇒ R...

1 Answers 1 views
In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: Find the value of x in the following expression. 33.33% of 342 + 12.5% of 800 + x = 40% of 900 Quantity B: What will come in place of question mark () in the following question 35% of (32 × 8 ÷ 16 ÷ 4)% of 10000 + √36 = ?

Option 5 : Quantity A = Quantity B or No relationQuantity A: 33.33% of 342 + 12.5% of 800 + x = 40% of 900 ⇒ (1/3) × 342 + (1/8) of 800...

1 Answers 1 views
X