Rates and Conversions | Quantitative Reasoning for UCAT PDF Download

Rate

• A rate is a ratio that compares two quantities with different units.
• It expresses how one quantity changes in relation to another quantity

Example: speed is a rate that compares distance and time (e.g., miles per hour or kilometers per hour).

Rate Calculation:
To calculate a rate, divide the quantity of interest by the unit of measurement.
Rate = Quantity of Interest / Unit of Measurement

Types of Rates

Example: If a car travels 200 kilometers in 4 hours, the speed rate is 200 km/4 hours = 50 km/h.

2. Growth Rate:
Growth rate measures the change in a quantity over time.

Example: If a population increases from 1000 to 1500 in 5 years, the growth rate is (1500 - 1000) / 5 = 100 people per year.

3.Interest Rate:
Interest rate measures the cost or return on an investment over a specific period.

Example: If $1000 invested in a savings account earns $50 in interest in one year, the interest rate is $50/$1000 = 5%.

Conversions

Common Unit Conversions:
Length:

• 1 meter (m) = 100 centimeters (cm)
• 1 meter (m) = 1000 millimeters (mm)
•  1 inch = 2.54 cm

Mass:

• 1 kilogram (kg) = 1000 grams (g)
• 1 kilogram (kg) = 1000000 milligrams (mg)
• 1 pound = 0.4536 kg.

Time:

• 1 hour (h) = 60 minutes (min)
• 1 hour (h) = 3600 seconds (s)

Volume:

• 1 liter (L) = 1000 milliliters (mL)
• 1 liter (L) = 1000 cubic centimeters (cm³)

Time, Distance and Speed:

• To convert from km / hour to m / sec, we multiply by 5 / 18. So, 1 km / hour = 5 / 18 m / sec
• To convert from m / sec to km / hour, we multiply by 18 / 5. So, 1 m / sec = 18 / 5 km / hour = 3.6 km / hour

Similarly, 1 km/hr = 5/8 miles/hour

• 1 yard = 3 feet
• 1 kilometer= 1000 meters = 0.6214 mile
• 1 mile= 1.609 kilometer
• 1 hour= 60 minutes= 60*60 seconds= 3600 seconds
• 1 mile = 1760 yards
• 1 yard = 3 feet
• 1 mile = 5280 feet
• 1 mph = (1 x 1760) / (1 x 3600) = 22/45 yards/sec
• 1 mph = (1 x 5280) / (1 x 3600) = 22/15 ft/sec

Currency Conversions

Basics of Currency Conversions

• Exchange rates: The value of one currency expressed in terms of another
  For example, 1 USD = 0.85 EUR (1 US Dollar is equivalent to 0.85 Euros)
• Direct and indirect quotes: Two ways of expressing exchange rates
• Direct quote: Home currency per unit of foreign currency
  Example: 1 EUR = 1.18 USD (1 Euro is equivalent to 1.18 US Dollars)
• Indirect quote: Foreign currency per unit of home currency
  Example: 1 USD = 0.85 EUR (1 US Dollar is equivalent to 0.85 Euros)

Performing Currency Conversions

• Simple conversion: Converting a given amount of one currency to another using the exchange rate
  Example: Convert 100 USD to EUR using the exchange rate 1 USD = 0.85 EUR
   Calculation: 100 USD * 0.85 EUR/USD = 85 EUR
• Cross rates: Exchange rates between two currencies not involving the home currency
  Example: Find the exchange rate between GBP (British Pounds) and EUR (Euros) using the exchange rates 1 USD = 0.85 EUR and 1 USD = 0.75 GBP
  Calculation: (1 EUR/USD) * (0.75 GBP/USD) = 0.64 GBP/EUR
• Reverse conversions: Converting from foreign currency to home currency
  Example: Convert 100 EUR to USD using the exchange rate 1 EUR = 1.18 USD
  Calculation: 100 EUR * 1.18 USD/EUR = 118 USD

Practice Problems

Given : Earning in 2.5 years = $7500
1 year = 12 months
2.5 years = 2.5(12) = 30 months
Then, earning in 30 months = $7500
Therefore, earning in 1 month = 7500/30
= $250

Q. 3. If John can cover 360 miles in 3 hours, find the number of miles covered by John in 1 minute.

No of miles covered in 3 hours = 360
Then, no. of miles covered in 1 hour = 360/3 = 120
1 hour = 60 minutes
So, no. of miles covered in 60 minutes = 120
Then, no. of miles covered 1 minute = 120/60
= 2 miles

Q.3. In 36.5 weeks, Miguel raised $2,372.50 for cancer research. How was his unit rate in price per week ?

Given : Miguel raised $2, 372.50 in 36.5 weeks
Then, amount raised in one week = (2372.5)/36.5
= $65

Q.4. If a person drinks 8 cups of apple juice per month, how many gallons will he drink in one year?

Given : 8 cups in one month
1 year = 12 months
So, no. of cups in 1 year = 8(12) = 96 cups
1 gallon = 16 cups
Therefore, no. of gallons in 1 year = 96/16
= 6 gallons

Q.5. 75 basketballs cost $1,143.75. Find the unit rate in price per basketball.

Given : 75 basketballs cost $1,143.75
Then, price of one basket ball = (1143.75)/75
= $15.25