Tayarri LCAT
LCAT Math, Problem-Solving and Data Analysis

Ratios, rates and units for the LCAT: lesson and practice

For ratio and rate questions, write the units on every number. Proportions keep the same units in the same position (cost/kg = cost/kg). A ratio a : b splits a total into a + b equal parts. For unit conversions, multiply by fractions that cancel the unwanted units.

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No calculator on the LCAT. LUMS’s official guidelines say calculators are not allowed, so every practice question here can be solved by hand.

Ratios

Example

Boys to girls is 3 : 5 and there are 40 students. How many girls?

3 + 5 = 8 parts
40 ÷ 8 = 5 students per part
girls = 5 × 5 = 25

Unit conversions

100 mL/min × 60 min/h × 3 h = 18,000 mL = 18 L

Each fraction cancels one unit. If the units do not cancel to the unit you want, the setup is wrong.

Combined rates

Add rates, not times. Pump A fills a tank in 3 hours (1/3 per hour), Pump B in 6 hours (1/6 per hour). Together: 1/3 + 1/6 = 1/2 per hour, so 2 hours.

Working together must be faster than the faster one alone. Use that to eliminate choices.

Common mistakes

Proportion upside downMatch units: cost/kg on both sides.
Part-to-part as part-to-wholeIn 3 : 5, girls are 5/8 of the total, not 5/3.
Forgetting a conversion stepHours to minutes, mL to L: write every unit.
Averaging times in work problemsAdd rates instead.

Sample questions with answers

1. If 3 kg of rice cost Rs 540, how much do 7 kg cost?
  1. Rs 1,080
  2. Rs 1,260 (correct)
  3. Rs 720
  4. Rs 231

540 ÷ 3 = 180 per kg, and 7 × 180 = 1,260.

2. The ratio of boys to girls is 3 : 5 and there are 40 students. How many are girls?
  1. 15
  2. 24
  3. 25 (correct)
  4. 35

8 parts of 5 students each; girls are 5 parts = 25.

3. Pump A fills a tank in 3 hours and Pump B in 6 hours. How long together?
  1. 4.5 hours
  2. 9 hours
  3. 2 hours (correct)
  4. 3 hours

1/3 + 1/6 = 1/2 tank per hour, so 2 hours.

Frequently asked questions

How do you set up a proportion on the LCAT?

Put the same units in the same position on both sides, such as cost/kg = cost/kg, then cross-multiply.

How do you convert units on the LCAT?

Multiply by conversion fractions so the unwanted units cancel, for example × 60 min/h to go from hours to minutes.

How do you solve work-rate problems?

Convert each time to a rate (jobs per hour), add the rates, then divide 1 by the total rate.

Is ratios, rates and units tested on the LCAT?

Yes. It falls under Problem-Solving and Data Analysis, one of the content domains LUMS lists for the LCAT in its official sample questions.

Can I practice this without a calculator?

Yes. Every practice question here can be solved by hand, because calculators are not allowed on the LCAT.

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