Question: A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 seconds and 10 seconds respectively. The length of the train (in meters) is

1. 45
2. 50
3. 54
4. 62
5. 72

Correct Answer: (B)
Solutions and Explanation
Approach Solution - 1 :

Let v m/s = train speed
Let L m = train length

For First person (2 km/h)

The first person travels (2*5/18*9) = 5 meters and the train has traveled 9 meters after 9 seconds.
=> 9v = 5 + L, Consider this as equation - (1)

For second person (4 km/h)

The second person moves (4*5/18*10) = 100/9 meters and the train moves 10 meters after 10 seconds.
=> 10v = 100/9 + L , Consider this as equation - (2)

By equations (2) - (1) => v = 55/9 m/s
(1) => 9v - 5 = L = 9(55/9) - 5 = 50 meters

Approach Solution - 2 :

Let t be the train's speed and x be its length.

The train's length is then (t-2)
We are aware that speed = distance/time, so it can also be written as distance = speed * time
In relation to a person moving at a speed of 2 kph, use *9/3600 and (t-4)*10/3600, respectively.

However, the length is the same, so (t-2)
9t - 18 = 10t - 40 = 22 kph *9/3600 = (t-4) *10/3600

Therefore, x = (22-2)*9/3600 = 0.050km = 50m

Approach Solution - 3 :

Consider the length of train as L and speed of train as S.

Speed of person 1 = 2 kmph = 5/9 m/s
Speed of person 2 = 4 kmph = 10.9 m/s

Now, we can write the following equations:

L / [s- (5/9)] = 9, and
L / [s- (10/9)] = 10

By solving the two equations, we can get two variables.

S = 55/9 and L = 50

“A train overtakes two persons who are walking in the same direction ” - is a subject covered in the GMAT quantitative reasoning section. A student needs to be knowledgeable in a wide range of qualitative skills in order to successfully complete GMAT Problem Solving questions. There are 31 questions in the GMAT Quant section overall. Calculative mathematical problems must be solved in the GMAT quant topics' problem-solving section using appropriate mathematical skills.

Suggested GMAT Problem Solving Samples

• At exactly what time past 7:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time? GMAT Problem Solving
• There is a 120 Liter Mixture of Alcohol and Water GMAT Problem Solving
• When X Is Divided By 13, The Answer Is Y With a Remainder of 3 GMAT Problem Solving
• If a/b = 2/3 Which of the Following is Not True? GMAT Problem Solving
• 1/3 of the Cookies in a Jar are Chocolate Chip, 2/3 of the Remaining Cookies are Peanut Butter GMAT Problem Solving
• The Kinetic Energy K, in Joules, Provided by the Mass of a Particle m GMAT Problem Solving
• A Recent Survey Showed That 50 Percent of People Polled Believe that Elected Officials Should Resign GMAT Problem Solving
• The Perimeter of a Square is Equal to the Perimeter of a Rectangle Whose Length And Width are 6m and 4m Respectively GMAT Problem Solving
• The Closing Price of Stock X Changed on Each Trading Day Last Month GMAT Problem Solving
• An Exam Consists of 8 True/False Questions GMAT Problem Solving
• From her Collection of 9 Different Hats Ellen Wants to Wear one Different Hat GMAT Problem Solving
• Company C Sells a Line of 25 Products with an Average Retail Price of $1,200 GMAT Problem Solving
• A Man has 1044 Candles. After Burning, He can Make a New Candle GMAT Problem Solving
• An Equilateral Triangle ABC is Inscribed in Square ADEF GMAT Problem Solving
• A Popular Website Requires Users to Create a Password Consisting of Digits Only GMAT Problem Solving
• A Furniture Store Sells Only Two Models of Desks, Model A and Model B GMAT Problem Solving
• In a Drawer, There are 4 White Socks, 3 Blue Socks, and 5 Grey Socks GMAT Problem Solving
• There are 100 Apples in a Bag of which 98% are Green and Rest are Red GMAT Problem Solving
• A palindrome is a number that reads the same forward and backward GMAT Problem Solving
• Three Cars Leave From A To B In Equal Time Intervals GMAT Problem Solving
• An Inlet Pipe can Fill in an Empty Cistern in 30 minutes GMAT Problem Solving
• Iqbal Dealt Some Cards to Mushtaq and himself from a Full Pack of Playing Cards GMAT Problem Solving
• A Zookeeper Counted the Heads of the Animals in a Zoo and Found it to be 80 GMAT Problem Solving
• A Shop Stores x kg of Rice. The First Customer Buys half this Amount Plus half a kg of Rice GMAT Problem Solving
• In a Class of 120 Students Numbered 1 to 120, All Even Numbered Students Opt for Physics GMAT Problem Solving
• Machine A Produces bolts at a Uniform Rate of 120 Every 40 seconds GMAT Problem Solving
• If The Average (arithmetic mean) of The Four Numbers 3, 15, 32, and (N + 1) is 18, then N = GMAT Problem Solving
• Out of 7 Consonants and 4 Vowels, How Many Words of 3 Consonants and 2 Vowels Can be Formed? GMAT Problem Solving
• 4 Bells Toll Together at 9:00 A.M. They Toll After 7, 8, 11 and 12 Seconds GMAT Problem Solving
• 12 Marbles are Selected at Random from a Large Collection of White, Red, Green and Yellow Marbles GMAT Problem Solving
• Find the greatest number that will divide 43, 91 and 183 GMAT Problem Solving
• Of the 150 Houses in a Certain Development GMAT Problem Solving
• A man can hit a target once in 4 shots. If he fires 4 shots in succession GMAT Problem Solving
• If 75 Percent of a Class Answered the First Question on a Certain Test Correctly GMAT Problem Solving
• A Clock Strikes 4 taking 9 seconds GMAT Problem Solving
• What is the Largest Power of 3 Contained in 200! GMAT Problem Solving
• Find The Value Of x GMAT Problem Solving
• 4 Out Of 15 Apples Are Rotten. They Are Taken Out One By One At Random GMAT Problem Solving
• Last Year 26 Members of a Certain Club Traveled to England, 26 Members Traveled to France, and 32 Members Traveled to Italy GMAT Problem Solving
• Running at the Same Constant Rate, 6 Identical Machines can Produce a Total of 270 Bottles Per Minute GMAT Problem Solving
• A Takes 5 More Days Than B To Do A Certain Job And 9 Days More Than C GMAT Problem Solving
• A Watch Which Gains 5 Seconds In 3 Minutes Was Set Right At 7 A.M. GMAT Problem Solving
• Of The 800 Employees Of Company X, 70 Percent Have Been With The Company GMAT Problem Solving
• To 100 Litres Of Milk, 10 Litres Of Water Is Added And Then 20 Litres GMAT Problem Solving
• Walking at 3/4 of his normal speed, Mike is 16 minutes late GMAT Problem Solving
• There are 12 yes or no questions. How many ways can these be answered? GMAT Problem Solving
• There are 7 Red and 5 Blue Marbles in a Jar GMAT Problem Solving
• A Basket Contains 3 White and 5 Blue Balls GMAT Problem Solving
• Working together, John and Jack can type 20 pages in one hour GMAT Problem Solving
• Is x^2 *x^5*z>0? GMAT Problem Solving