Quantitative Aptitude – Geometry – Rajesh, a courier delivery agent

XAT 2021 Exam Paper – Quantitative Aptitude – Geometry – Rajesh, a courier delivery agent

Q. Rajesh, a courier delivery agent, starts at point A and makes a delivery each at points B, C and D, in that order. He travels in a straight line between any two consecutive points. The following are known:
(i) AB and CD intersect at a right angle at E, and
(ii) BC, CE and ED are respectively 1.3 km, 0.5 km and 2.5 km long.
If AD is parallel to BC, then what is the total distance (in km) that Rajesh covers in travelling from A to D?

1. 10.2
2. 12
3. 5.5
4. 11.5
5. 18

Answer: 11.5

Solutions:

Given, CE=0.5, BC = 1.3 and ED=2.5
Triangle CEB is a right-angled triangle, Using Pythagoras Theorem EB = 1.2
Now triangle ECB is similar to triangle EDA
So EB/EC = AE/ED => AE = 6
Hence total distance travelled = AB + BC + CD = 7.2 + 1.3 + 3 = 11.5 km

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