Question: Ram and Shyam travel the same distance at the speeds of 10 kmph and 15 kmph respectively. If Ram takes 30 min longer than Shyam, then the distance travelled is

1. 30 km
2. 20 km
3. 15 km
4. 10 km
5. 2 km

Correct Answer: C
Solution and Explanation:
Approach Solution 1:

The problem statement states that:

Given:

• Ram and Shyam travel the same distance at the speeds of 10 kmph and 15 kmph respectively.
• Ram takes 30 min longer than Shyam.

Find out:

• The distance travelled by them.

Let the distance travelled by Ram and Shyam be D.

Speed of Ram to travel the same distance = 10 kmph
Therefore, time taken by Ram = Distance/Speed (as per the formula) = D/10 hr

Speed of Shyam to travel the same distance = 15 kmph
Therefore, time taken by Shyam = Distance/Speed (as per the formula) = D/15 hr

Therefore, the difference between the time taken by Ram and Shyam

= D/10 – D/15 hr
= 3D - 2D/ 30 hr
= D/30 hr
= D ∗ 60/30 min = 2 ∗ D

According to the given condition of the question,
Ram takes 30 min longer than Shyam
Therefore, we can say,
2 ∗ D = 30
D = 30/2 =15 km.
Hence, the distance travelled by Ram and Shyam is 15 km.

Approach Solution 2:

The problem statement informs that:

Given:

• Ram and Shyam travel the same distance at the speeds of 10 kmph and 15 kmph respectively.
• Ram takes 30 min longer than Shyam.

Find out:

• The distance travelled by them.

Let the speed of Ram = 10 kmph = S1
Let the speed of Shyam = 15 kmph = S2

Let, time taken by Ram = T1
Let, time taken by Shyam = T2

Ram takes 30 mins longer than Shyam, this implies that T1 = T2 + 30 (where T1, T2 are in minutes).... (i)

Since Ram and Shyam travel the same distance, the distance is constant
T1/T2 = S2/S1 (since distance= speed * time)
=> T1/T2 = 15/10 = 3/2
=> 2*T1 = 3*T2

Substituting the value of T1 from equation (i), we get:
2 (T2 + 30) = 3T2
2*T2 + 60 = 3*T2
T2= 60 mins = 1hour

S2= 15 kmph
Distance = Speed * Time
Distance= 15 * 1 kms
Distance= 15 kms

Hence, the distance travelled by Ram and Shyam is 15 kms.

Approach Solution 3:

The problem statement suggests that:

Given:

• Ram and Shyam travel the same distance at the speeds of 10 kmph and 15 kmph respectively.
• Ram takes 30 min longer than Shyam.

Find out:

• The distance travelled by them.

Let the time taken by Shyam = t hours
Ram takes 30 min longer than Shyam
Therefore, the time taken by Ram = t + 0.5 hours (since 30 min= 30/60 = ½ = 0.5 hour)

Let the distance travelled by Ram and Shyam be x km.
Speed of Ram = 10 kmph
Therefore, time taken by Ram = Distance/Speed (as per the formula) = x/10 hour
Speed of Shyam = 15kmph
Therefore, the time by Shyam = x/15 hour

Hence, we can say,
x/10 = t + 0.5 —-- (i)
x/15 = t —-- (ii)

Simplifying both equations we get:
x/10 = x/15 + 0.5
x = 30 × 0.5
x = 15

Hence, the distance travelled by Ram and Shyam is 15 kms.

“Ram and Shyam travel the same distance at the speeds of 10 kmph and 15”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT Problem Solving questions enable the candidates to consider minute data given in the question in order to solve numerical problems. GMAT Quant practice papers help the candidates to analyse several sorts of questions that will allow them to improve their mathematical knowledge.

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