Question

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.

Answer 1

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

Answer 2

Step-by-step explanation:

BIG BUT EASY TO UNDERSTAND

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