XAT 2021 — QA & DI Question 7
Basics of TSD/ProportinalityEasy
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?
Answer & solution
- A
10.2
- B
12
11.5
- D
5.5
- E
18
Solution
Given, CE = 0.5, BC = 1.3 and ED = 2.5
Triangle CEB is a right-angled triangle ⇒ EB = 1.2
Triangles ECB is similar to triangle EDA
EB/EC = AE/ED ⇒ AE = 6
Hence total distance travelled = AB + BC + CD = 7.2 + 1.3 + 3.5 = 11.5km