CAT 1994 — QA Question 32
Answer the next 3 questions based on the information given below:
Alphonso, on his death bed, keeps half his property for his wife and divide the rest equally among his three sons Ben, Carl and Dave. Some years later Ben dies leaving half his property to his widow and half to his brothers Carl and Dave together, shared equally. When Carl makes his will he keeps half his property for his widow and the rest he bequeaths to his younger brother Dave. When Dave dies some years later, he keeps half his property for his widow and the remaining for his mother. The mother now has Rs. 1,575,000.
Data is provided followed by two statements – I and II – both resulting in a value, say I and II.
As your answer,
Type 1, if I > II.
Type 2, if I < II.
Type 3, if I = II.
Type 4, if nothing can be said.
In ΔACD, AD = AC and ∠C = 2∠E. The distance between parallel lines AB and CD is h. Then
I. Area of parallelogram ABCD
II. Area of ΔADE
Answer & solution
Answer: 3
Since ∠C = 2 ∠E , therefore ∠BCA = 60°.
Also since ABCD is a parallelogram,
AB = CD and AD = BC = AC.
Hence, ΔABC and ΔACD are equilateral triangles.
Hence, area of this triangle =
where s is the side of the triangle = AB = AD = DC = BC.
∴ Area of the parallelogram is twice this area =
Since ∠CAD = 60°, ∠DAE = 90°, so ΔEAD is a right triangle with side AD = s. Since it is a 30-60-90 triangle, hence side AE = s
∴ Area of this triangle =
Hence, the required two areas are equal or I = II.