# CAT 2021 Question Paper | Quant Slot 3

###### CAT Previous Year Paper | CAT Quant Questions | Question 12

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

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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

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