If cost of constructing a path of uniform width around a circular garden of diameter 50 meter at the rate of Rs. 350 per meter sq. is Rs. 144375, then width of a path is:
OPtion
1) 350 cm
2) 225 cm
3) 300 cm
4) 275 cm
5) 260 cm
6) 325 cm
7) 250 cm
8) 370 cm
9) 200 cm
10) None of these
Solution
Radius of garden r = 50/2 = 25 m.
Let the width of a circular path=x m, then outer radius=(25+x) m.
Area of a path = Total Cost/Rate per m. sq. = 144375/350 = 412.5 m. sq.
Also, Area of a path = Area of a outer circle - Area of inner circle = π[(25+x)² - 25²]
⇒ π[(25+x)² - 25²] = 412.5
(22/7)*[625 + 50x + x² - 625] = 412.5
4x² + 200x - 525 = 0
4x² + 210x - 10x - 525 = 0
(2x-5) (2x+105) = 0
⇒ x=5/2, -52.5
Considering +ve value, x=5/2 or 2.5 m=250 cm
Correct Option 7)
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john adams
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