CAT 2021 Question Paper | Quant Slot 3

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 12 : A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of ₹125 per m, is

Video Explanation

Explanatory Answer

The are of the rhombus is given by,
Area = ½ × d₁ × d₂
Where d₁ & d₂ are the diagonals of the rhombus.

Area = ½ × d₁ × d₂
96 = ½ × d₁ × d₂
96 × 4 = 2 × d₁ × d₂
Also,
\( \left( \frac { d _ { 1 } } { 2 } \right) ^ { 2 } + \left( \frac { d _ { 2 } } { 2 } \right) ^ { 2 } = 10 ^ { 2 } \)
d₁² + d₂² = 400
(d₁ + d₂ )² = d₁² + d₂² + 2 × d₁ × d₂
(d₁ + d₂ )² = 400 + 4(96)
(d₁ + d₂ )² = 4(100 + 96)
(d₁ + d₂ )² = 4(196)
(d₁ + d₂) = 2(14)
d₁ + d₂ = 28
The cost of laying electric wires along the diagonals at the rate of ₹125 per meter
= 28 × 125
= ₹3500

The answer is '3500'