# GMAT Quant: Word Problems Formula

Word Problems in GMAT Quant consists of the following topics. Time Speed (Rate) Problems, Work Problems, Mixture Problems, Interest Problems, Discount, Profit, Sets and Venn Diagrams, Geometry Problems, Measurement Problems, Data Interpretation.

The Formulas for the same are as follows –

## Time Speed Distance & Rate Formulas

$Distance = Time \times Speed$

$Time = \frac{Distance}{Speed}$

$Speed = \frac{Distance}{Time}$

$Average \; Speed = \frac{Total \; Distance}{Total \; Time}$

$Distance = Rate \times Time$

$Distance = Rate \times Time$

$Time = \frac{Distance}{Rate}$

## Shortcut Tips & Formulas to Solve Time, Speed & Distance Problems Faster

1. Km/hr to m/sec Conversion

$x \; Km/hr = \left ( x \times \frac{5}{18} \right ) m/sec$

1. m/sec to km/hr Conversion

$x \; m/sec = \left ( x \times \frac{18}{5} \right ) km/hr$

1. If the ratio of the speeds of A and B is a : b, then the ratio of the

the time taken by them to cover the same distance is –

$\frac{1}{a} : \frac{1}{b} \; or \; b:a$

1. If a train covers a certain distance x km/hr and an equal distance at y km/hr. Then,

Average Speed during the whole journey is $\left ( \frac{2xy}{x + y} \right ) \; km/hr$

## Work Problems – Formula

$Rate \; of \; Work = \frac{Total \; Work}{Time \; Taken}$

Suppose a person A works for N days, then he can do 1/N of the work in 1 day.

Similarly, suppose another person B works for M days, then he can do 1/M of the work in 1 day.

$()Rate \; of \; A) + )Rate \; of \; B) = (Combined \; Rate \; of A \; \& \; B )$

## Mixture Problems – Formula

Rule of Alligation

If two ingredients are mixed, then

$\left ( \frac{Quantity \; of \; Cheaper}{Quantity \; of\; Dearer} \right ) = \left ( \frac{Cost \; price \; of \; Dearer – Mean \; Price}{Mean \; Price – Cost \; price \; of \; Cheaper} \right )$

Which is as follows:

$(Cheaper \; Quantity) : (Dearer \; Quantity) = (d – m) : (m – c)$

## Interest Problems – Formula

$SI = \frac{P \times R \times T}{100}$

$New \; Principle \; Amount = P + SI$

$CI = P \times \left ( 1 + \frac{R}{100} \right )^{T} – P$

$New \; Principle \; Amount = P + CI$

Where,

P: Principle amount that has been borrowed

R: Rate of interest charged to the borrower

T: Time span for which the borrower has borrowed money

SI: Simple interest

CI: Compound interest

## Discount Formula

$Discount \; \% = \frac{Marked \; Price – Selling \; Price}{Marked \; Price} \times 100$

Where, Marked price (MP): The initial quoted price

Selling price (SP): The Price which you pay after getting discounts.

Cost Price (CP): The price at which the shopkeeper purchased the good or the amount that the seller expend to manufacture the good.

## Percent Formulas

Converting Percentage into Decimal

$20 \% = \frac{20}{100} = 0.5$

Converting Decimal Into Percentage

$0.25 = (0.25 \times 100) \% = 25 \%$

$1.50 = (1.50 \times 100) \% = 150 \%$

Percent Change

$Percent \; Change = \frac{(End \; Value) – (Start \; Value)}{(Start \; Value)} * 100$

$Percent \; Change (as \; decimal)= \frac{(End \; Value) – (Start \; Value)}{(Start \; Value)}$

Percentage Increase/Decrease

If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:

$\left [ \frac{R}{(100 + R)} \times 100 \right ]\%$

If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:

$\left [ \frac{R}{(100 – R)} \times 100 \right ]\%$

Percentage Formula for Population Sums

For Present Population P and suppose it increases at the rate of R% per annum, then:

$Population \; after \; n \; years = P \left ( 1 + \frac{R}{100} \right )^{n}$

$Population \; n \; years \; ago = \frac{P}{\left ( 1 + \frac{R}{100} \right )^{n}}$

## Profit & Loss Formulas

Cost price (CP) is the price at which an article is purchased.

Selling price (SP) is the price at which an article is sold.

If SP > CP, it is a profit or gain

If CP > SP, it is a loss.

Gain or Profit = SP – CP

Loss = CP – SP

Loss or gain is always reckoned on CP

Profit Percentage (Profit %)

$\frac{Profit}{CP} \times 100 = \frac{(SP – CP)}{CP} \times 100$

Loss Percentage (Loss %)

$\frac{Loss}{CP} \times 100 = \frac{(CP – SP)}{CP} \times 100$

In the case of a gain or profit,

$SP = \frac{(100 + Gain \%)}{100} \times CP$

$CP = \frac{100}{(100 + Gain \%)} \times SP$

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