SarkariPYQ

SSC CGL 2020 PYQ — Question 63

SSC CGL - 3rd March 2020 Shift 1 • Quantitative Aptitude • Q63

Back to paper

In ΔABC, MN || BC, the area of quadrilateral MBCN = 130 sqcm. If AN : NC = 4 : 5, then the area of ΔMAN is:

Show answer & explanation

Correct answer: A

Explanation

The correct answer is Option 1 i.e. 32 cm2

Application

Given fig:

In ΔABC & ΔAMN

∠A = ∠A (common angle)

∠ABC = ∠AMN (Corresponding angle)

So

ΔABC ~ ΔAMN (A-A)

Now,

ar ΔABC/arΔAMN = (AC/AN)2

⇒ (area of qua.MBCN + arΔAMN)/arΔAMN = (9/4)2

⇒ (130 + arΔAMN)/arΔAMN = 81/16

⇒ (2080 + 16 × arΔAMN) = 81 × arΔAMN

⇒ (2080) = 65 × arΔAMN

Hence,

arΔAMN = 2080/65 = 32