Following are some important formulas for Arithmetic Skills section of the VRO and VRA recruitment examination. There will be 30 questions for 30 marks for Arithmetic Skills in VRO and VRA written exams. Candidates can download comprehensive study material on Arithmetic Skills from the link given at the end of these formulas:

**Time and Work Formulas**

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

2) If A’s 1 day’s work = 1/n, then A can finish the work in n days.

3) 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 & B to finish a work = 1 : 3

**Trains and Speed Formulas**

1) Lengths of trains are ‘x’ km and ‘y’ km, moving at ‘u’ kmph and ‘v’ kmph (where, u > v) in the same direction, then the time taken y the over-taker train to cross the slower train is

[(x + y) / (u - v)] hrs

2) Time taken to cross each other is [(x + y) / (u + v)] hrs

**Finding Discount:**

Suppose a man has to pay Rs. 156 after 4 years and the rate of interest is 14% per

annum. Clearly, Rs. 100 at 14% will amount to Rs. 156 in 4 years. So, the payment of

Rs. 100 now will clear off the debt of Rs. 156 due 4 years hence. We say that:

Sum due = Rs. 156 due 4 years hence;

Present Worth (P.W.) = Rs. 100;

True Discount (T.D.) = Rs. (156 - 100)

= (Sum due) – (P.W.)

T.D. = Interest on P.W.

Amount = (P.W.) + (T.D.)

Interest is reckoned on R.W. and true discount is reckoned on the amount

Let rate = R% per annum & time = T years. Then,

a. P.W. = (100 × Amount) / (100 + [R × T])

= (100 × T.D.) / (R × T)

b. T.D. = (P.W.) × R × T / 100

= ([Amount] × R × T) / (100 + [R × T])

c. Sum = ([S.I.] × [T.D.]) / ([S.I.] – [T.D.])

d. (S.I.) – (T.D.) = S.I. on T.D.

e. When the sum is put at compound interest, then

P.W. = Amount / (1 + R/100)T

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