Maths formulas # 01 :)

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PROBLEMS ON TRAINS

1. km/hr to m/s conversion:

a km/hr =		a x	5		m/s.
			18

2. m/s to km/hr conversion:

a m/s =		a x	18		km/hr.
			5

Formulas for finding Speed, Time and Distance

• Time taken by a train of length l metres to pass a pole or standing man or a signal post is equal to the time taken by the train to cover l metres.

• Time taken by a train of length l metres to pass a stationery object of length b metres is the time taken by the train to cover (l + b) metres.

• Suppose two trains or two objects bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed is = (u - v) m/s.

• Suppose two trains or two objects bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s.

• If two trains of length a metres and b metres are moving in opposite directions at um/s and v m/s, then:

The time taken by the trains to cross each other =	(a + b)	sec.
	(u + v)

• If two trains of length a metres and b metres are moving in the same direction at um/s and v m/s, then:

The time taken by the faster train to cross the slower train =	(a + b)	sec.
	(u - v)

•   If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then:

(A's speed) : (B's speed) = (b : a)

TIME AND WORK

1. Work from Days:

If A can do a piece of work in n days, then A's 1 day's work =	1	.
	n

2. Days from Work:

If A's 1 day's work =	1	,	then A can finish the work in n days.
	n

3. Ratio:

If A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3 : 1.

Ratio of times taken by A and B to finish a work = 1 : 3.

Pipes and Cistern

1. Inlet:

A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.

Outlet:

A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.

2. If a pipe can fill a tank in x hours, then:

part filled in 1 hour =	1	.
	x

3. If a pipe can empty a tank in y hours, then:

part emptied in 1 hour =	1	.
	y

4. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then

the net part filled in 1 hour =		1	-	1		.
		x		y

5. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where x > y), then on opening both the pipes, then

the net part emptied in 1 hour =		1	-	1		.
		y		x