Question: A man travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes. But if he travels 200 km by train and the rest by car, he takes half an hour longer. Find the speed of the train (T) and that of the car (C) in km/h.

       A. T = 120, C = 100
       B. T = 200, C = 180
       C. T = 60, C = 50
       D. T = 80, C = 60
       E. T = 100, C = 80

Answer: E

Approach Solution (1):
Let the speed of a train = x km/hr
And the speed of a car = y km/hr
Total distance travelled = 600km
According to the question,
If he covers 400km by train and rest by car i.e. (600 – 400) = 200km
Time take = 6hrs 30min = 6 + 30/60 = 6.5 hrs
If he travels 200km by train and rest by car i.e. (600 – 200) = 400km
He takes half hour longer i.e. 7 hours
So, total time = train time + car time
We know that,
Time = Distance /Speed
= 400/x + 200/y = 6.5 – (1)
= 200/x + 400/y = 7 – (2)
Let us take 1/x = u , 1/y = v
400u + 200v = 6.5 …(iii)
and 200u + 400v = 7 …(iv)
On multiplying Eq. (iii) by 2 and Eq. (iv) by 4, we get
800u + 400v = 13 …(a)
800u + 1600v = 28 …(b)
On subtracting Eq. (a) from Eq. (b), we get
800u + 1600v – 800u – 400v = 28 – 13
⇒1200v = 15
⇒ v= 15/1200
⇒ v = 1/80
On putting the value of v in Eq. (iv), we get
200u + 400(1/80) = 7
⇒200u + 5 = 7
⇒200u = 2
⇒ u = 1/100
So we get
u = 1/100 and v = 1/80
⇒x = 100 and y = 80
Hence, the speed of the train is 100km/hr and the speed of the car is 80km/hr
Correct option: E

Approach Solution (2):
Step 1 of 3
Given A man travels 600km partly by train and partly by car, it takes 6 hours and 30 minutes. If he travels 400km by train and the rest by car, it would take 30 minutes more if he travels 200km by train and the rest by car.
To Find: The speed of the train and car separately.

Step 2 of 3

Step 3 of 3

Correct option: E

Approach Solution (3):
Let the speed of the train be‘x’ km/hrand the speed of the car be‘y’ km/hr.
It is given that he travels400 km partly by trainand the rest i.e. (600-400) = 200 km by car
To travels this distance he takes 6 hours 30 minutes which is equal to (6 + 30/60) = 13/2 hours
Also it is given that he travels 200 km by train and the rest i.e. (600-200) = 400 km by car and the time taken is half an hour longer i.e. (13/2 + 1/2)=7 hours
Distance = Speed × Time
Now,
400/x + 200/y = 13/2→ equation 1
200/x + 400/y = 7→ equation 2
Multiplying Equation 2 with 2 we get
400/x + 800/y = 14→ equation 3
Subtracting [Equation 3] from [Equation 2] we get,
Now substituting the value of y in [Equation 2] we get
Thus the speed of the train is100 km/hr and speed of the car is 80 km/hr.
Correct option: E

“A man travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes. But if he travels 200 km by train and the rest by car, he takes half an hour longer. Find the speed of the train (T) and that of the car (C) in km/h.?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Suggested GMAT Problem Solving Questions:

• Is Square Root = Always Positive? GMAT Problem Solving
• \(\frac{15^{11}-15^{10}}{14}=?\) GMAT Problem Solving
• For How Many Values of k is 12¹² the Least Common Multiple GMAT Problem Solving
• A Contractor Estimated that his 10-Man Crew Could Complete the Construction in 110 Days if There Was no Rain. GMAT Problem Solving
• If n = \(3^8\)– \(2^8\), Which of the Following is Not a Factor of n? GMAT Problem Solving
• Two Consultants, Mary and Jim, Can Type up a Report in 12.5 Hours and Edit it in 7.5 Hours. GMAT Problem Solving
• GMAT Problem Solving - The Price of Raw Materials Has Gone up by 15%
• Greg Assembles Units of a Certain Product at a Factory. GMAT Problem Solving
• After 6 Games, Team B Had an Average of 61.5 Points Per Game. GMAT Problem Solving
• Find The Number Of Trailing Zeros In The Product Of (1¹) GMAT Problem Solving
• Find The Altitude Of An Equilateral Triangle Whose Side is 20 GMAT Problem Solving
• Which of the following is the value of √3√0.000064? GMAT Problem Solving
• Two Dice are Thrown Simultaneously. What is the Probability of Getting Two Numbers Whose Product is Even? GMAT Problem Solving
• The Smallest 3-Digit Positive Integer Obtained By Adding Two Positive Two-Digit Numbers GMAT Problem Solving
• Train A Leaves New York at 9am Eastern Time on Monday, Headed for Los Angeles at a Constant Rate GMAT Problem Solving
• An Express Train Traveled At An Average Speed of 100 Kilometers Per Hour GMAT Problem Solving
• If m Lies Between The Integers p and s On the Number Line Shown GMAT Problem Solving
• A Cube Of Side 7 cm Is Coloured On Pair of Opposite Faces By Red, Green and Yellow Shades GMAT Problem Solving
• If x^2 − 5x − 6 = 0, which of the following could be x ? GMAT Problem Solving
• How Many Numbers Between 1 and 1000, Inclusive Have an Odd Number of Factors? 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
• 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
• 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
• GMAT Problem Solving - Which of the following expressions has the greatest values?
• GMAT Problem Solving – If @ x=x²/2x²-2 , What is the Units Digit of @ (@4)?
• GMAT Problem Solving – What is the product of all possible solutions of the equation |x+2|- 5|x+2| = -6?
• GMAT Problem Solving – Metropolis Corporation has 4 Shareholders
• GMAT Problem Solving – What is the number of integers from 1 to 1000, inclusive that are not divisible by 11 or by 35?
• GMAT Problem Solving – If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m?
• GMAT Problem Solving – If Ben Were to Lose the Championship, Mike would be the Winner
• GMAT Problem Solving – A Train Travelling at a Certain Constant Speed takes 30 seconds
• GMAT Problem Solving –A circle with a radius R is inscribed into a square with a side K.
• GMAT Problem Solving –The square of \(5^\sqrt2)\ =?
• GMAT Problem Solving –A farm has chickens, cows and sheep.
• GMAT Problem Solving –If g is an integer what is the value of (-1)^g^4-1?
• GMAT Problem Solving –What is the area of the triangle with the following vertices L(1,3) M(5,1) and N(3,5)?