CAT 2006 — QA Question 25
Answer the following question based on the information given below.
An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs. 5400.
An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees?
Answer & solution
- A
75
- B
90
- C
120
- D
135
150
BP = PC = BC
m ∠BPC = m ∠PCB = m ∠PBC = 60°
Also, PC = CD = BP = AB
â ABP and â PCD are isosceles triangles.
m ∠ABP = m ∠PCD = 90 – 60 = 30°
∴ m ∠APB = m ∠DPC = (180 – 30)/2 = 75°
∴ m ∠APD = 360 – (m ∠APB + m ∠DPC + m ∠BPC) = 360 – (75 + 75 + 60) = 150°
Hence, option (e).