GATE 2020 MA – Question 8

General Aptitude · Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation · 2 marks · Multiple choice

Delhi and Agra are 233 km apart. P travels from Delhi to Agra; Q starts from Agra to Delhi one hour later. They meet 75 minutes after Q starts. Both speeds are constant, and P is 10 km/h faster. How far has Q travelled when they meet?

66.6 km
75.2 km
88.2 km
116.5 km

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Correct answer: (B) 75.2 km

Explanation

Let Q’s speed be v km/h. Travel times at meeting are 1.25 h for Q and 2.25 h for P. Their distances add to 233: $1.25v+2.25(v+10)=233$. Hence $3.5v=210.5$, so $v=60.142857$ km/h. Q travels $1.25v=75.1786$ km, approximately 75.2 km, B.

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