Question: A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds. What is the length of the train in metres?
- 375 m
- 750 m
- 250 m
- 800 m
- 300 m
‘A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds’ 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.
Solution and Explanation
Approach Solution 1:
Given:
- A train crosses a bridge of length 500 m in 40 seconds
- The train crosses a lamp post on the bridge in 15 seconds.
Find Out:
- What is the length of the train in metres
Let us consider that the Length of Train = L
Case-1 (Bridge)
Distance = 500+L (While crossing the bridge)
Time = 40 Seconds
i.e. Speed = Distance / Time
= (500+L)/40
Case-2 (Lamp Post)
Distance = L (While passing the lamp post)
Time = 15 Seconds
i.e. Speed = Distance / Time
= (L)/15
But Since speed has to be same in both cases so, the speed of crossing lamp posi is equal to speed of crossing bridge.
Hence, we get:
(500+L)/40 = (L)/15
i.e. 8L = 3L + 1500
i.e. 5L = 1500
i.e. L = 300
Hence, the correct option is E.
Correct Answer: E
Approach Solution 2:
Given:
- A train crosses a bridge of length 500 m in 40 seconds
- The train crosses a lamp post on the bridge in 15 seconds.
Find Out:
- What is the length of the train in metres
Let the Length of train=LT
Let the Speed of train=VT
Time taken =(Length of train +Length of Bridge)/Speed of Train
40=(LT+500)VT
And, LT/VT=15
Let us now Put LT/VT=15 in the first equation,
15+500/VT=40
VT=20
Using value of VT=20, LT=300M
Hence, E is the correct answer.
Correct Answer: E
Approach Solution 3:
Let Length of Train be L
Let the first case be Distance be 500+L (While crossing the bridge)
Time = 40 Seconds
So, Speed = Distance / Time = (500+L)/40
Let the second case be Distance be L (While passing the lamp post)
Time = 15 Seconds
So, Speed = Distance / Time = (L)/15
Since speed has to be same in both cases so equating both the cases:
(500+L)/40 = (L)/15
that implies 8L = 3L + 1500
that implies 5L = 1500
that implies L = 300
Correct Answer: E
Suggested GMAT Problem Solving Questions
- 1511−151014=? GMAT Problem Solving
- If g is an integer what is the value of(−1)g4−1(−1)g4−1? GMAT Problem Solving
- What is the Area of the Triangle with the following Vertices L(1,3) M(5,1) and N(3,5)? GMAT Problem Solving
- If P2−QR=10P2−QR=10 ,Q2+PR=10Q2+PR=10 ,R2+PQ=10R2+PQ=10 GMAT Problem Solving
- If y (u-c) = 0 and j (u-k) = 0, Which of the Following Must be True, Assuming c < kc < k? GMAT Problem Solving
- If 298=256L+N298=256L+N , Where L and N are Integers and 0≤N≤40≤N≤4 GMAT Problem Solving
- How Many 5-Letter Words can be Formed Using the Letters of the English Alphabet GMAT Problem Solving
- If a+b+c = 0 and a^3+b^3+c^3 = 216, What is the Value of a∗b∗c ? GMAT Problem Solving
- If a Polygon has 44 Diagonals, Then How Many Sides are There in the Polygon? GMAT Problem Solving
- If (a1 + a2 + a3 + .... +an) = 3(2n+1 - 2), For Every n≥1, Then a11 Equals GMAT Problem Solving
- A Chord of a Circle is Equal to its Radius GMAT Problem Solving
- A Clock loses a Minute Every Three Hours for 4 Days GMAT Problem Solving
- A Container in the Shape of a Right Circular Cylinder is 1/2 Full of Water. GMAT Problem Solving
- How Many Multiples of 7 are there Between 21 and 343, Exclusive? GMAT Problem Solving
- How many Terminating Zeroes does 200! Have? GMAT Problem Solving
- What is the Remainder when 333^222 is Divided by 7? GMAT Problem Solving
- In a College of 300 Students, Every Student Reads 5 Newspapers GMAT Problem Solving
- If 4 People are Selected from a Group of 6 Married Couples, GMAT Problem Solving
- If the Equation |x|+|y|= 5 Encloses a Certain Region on the Graph GMAT Problem Solving
- If x = ¾ and y = ⅖ , What is the Value of √(x2+6x+9)(x2+6x+9) - √(y2−2y+1)(y2−2y+1)? GMAT Problem Solving
Comments