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Aptitude Formulae

Banker's Discount:

Suppose a merchant A buys goods worth, say Rs. 10,000 from another merchant B at a credit of say 5 months. Then, B prepares a bill, called the bill of exchange. A signs this bill and allows B to withdraw the amount from his bank account after exactly 5 months.

The date exactly after 5 months is called nominally due date. Three days (known as grace days) are added to it get a date, known as legally due date.

Suppose B wants to have the money before the legally due date. Then he can have the money from the banker or a broker, who deducts S.I. on the face vale (i.e., Rs. 10,000 in this case) for the period from the date on which the bill was discounted (i.e., paid by the banker) and the legally due date. This amount is know as Banker's Discount (B.D.).

Thus, B.D. is the S.I. on the face value for the period from the date on which the bill was discounted and the legally due date.

Banker's Gain (B.G.) = (B.D.) - (T.D.) for the unexpired time.

Note: When the date of the bill is not given, grace days are not to be added.

IMPORTANT FORMULAS

1.   B.D. = S.I. on bill for unexpired time.

2.   B.G. = (B.D.) - (T.D.) = S.I. on T.D. =  (T.D.)2 P.W.

3.   T.D. P.W. x B.G.

4.   B.D. = Amount x Rate x Time/100

5.   T.D. =Amount x Rate x Time/  100 + (Rate x Time)

6.   Amount = B.D. x T.D/B.D. - T.D.

7.   T.D. = B.G. x 100/Rate x Time

Clocks Synopsis 

1.    Minute Spaces:

The face or dial of watch is a circle whose circumference is divided into 60 equal parts, called minute spaces.

Hour Hand and Minute Hand:

A clock has two hands, the smaller one is called the hour hand or short hand while the larger one is called minute hand or long hand.

2. i. In 60 minutes, the minute hand gains 55 minutes on the hour on the hour hand.

     ii. In every hour, both the hands coincide once.

     iii. The hands are in the same straight line when they are coincident or opposite to each other.

     iv. When the two hands are at right angles, they are 15 minute spaces apart.

     v. When the hands are in opposite directions, they are 30 minute spaces apart.

     vi. Angle traced by hour hand in 12 hrs = 360°

     vii. Angle traced by minute hand in 60 min. = 360°.

     viii. If a watch or a clock indicates 8.15, when the correct time is 8, it is said to be        15 minutes too fast.

On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow.

Time 

Time And Work Synopsis

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

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