Quantitative aptitude · lesson 19 of 30 · free

Time and work — Quantitative aptitude for kids

If Aarav finishes a job in 10 days and Diya in 15, how long together? Call the job 30 units (the LCM). Aarav does 3 units a day, Diya 2, so together 5 a day: 30 ÷ 5 = 6 days. No messy fractions!

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The method

LCM units — “call the whole job the LCM of the days; then each person does a whole number of units a day”

  1. Take the whole job as the LCM of the days.
  2. Units a day for each person = job ÷ their days. Add for working together.
  3. Days = job ÷ units a day. The answer can be a fraction like 20/9 days.
  4. Someone works a few days and stops: find what is left, then share it out.

Use it for: Group projects, workers and machines, and time-and-work questions in aptitude and scholarship tests.

Worked example: Aarav can finish a job in 10 days and Diya in 15 days. How many days will they take working together? Give a fraction if the answer is not a whole number. → 6

  1. Job = 30 units (LCM of 10 and 15). Aarav does 3 a day, Diya does 2 a day: 5 units a day together.
  2. Days = 30 ÷ 5 = 6.

Check: In 6 days Aarav does 6/10 and Diya 6/15 = 3/5 + 2/5 = the whole job ✓

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🏁 Lesson 19 test

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🖨️ Time and Work Worksheet

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