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the fore wheel of a carriage makes 6 revolution more than the rear wheel in going 120m .If the diameter of the fore wheel be increased by 1/4 its present and the daimeter of the rear wheel be increased by one-fifth of its present diameter than the fore wheel makes 4 revolution more than the rear wheel in going the same distance. find the circumference of each wheel of the carriage. |
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Answer» LET the DIAMETER of the forewheel and rear wheel be d1 and d2 respectively.The circumference of each wheel = 1 revolution. if the carrier goes 120m then, 120/ πd1 = 120/πd2 + 6 → (1) 120/π 5d1 /4= 120/ *6 πd2/5 + 4 → (2) simplifying each of the EQUATIONS we get, 20*d2 = (20 d1 + d1*d2 *π) →(3) 24 d2 = (25d1+d2*d1*π) → (4) solving (3) and (1) d1 = (20*d2/(20+d2*π) substitute d1 in eq 4 (24*d2)= (25 *d2*π*(20*d2/(20+d2*π) solve for d2 now, d2 =5/ π d1= (20/5π)/ (20 +(5/π)*π) = 4/π circumference c for forewheel is π*d1 = 4m c for rear wheel is πd2 = 5M |
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