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Mixtures & Alligation · Question 21 of 60

Question 21

MediumOriginal question

A coaching batch of 45 students averaged 64 marks in a mock test. The boys averaged 60 and the girls averaged 69. How many girls are in the batch?

Options for question 21

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. Boys : girls = (69−64):(64−60)=5:4(69 - 64) : (64 - 60) = 5 : 4.

  2. Total parts = 9, so 1 part = 45÷9=545 \div 9 = 5 students.

  3. Girls = 4×5=204 \times 5 = 20.

Worth noting

25 is the number of boys. Check: 25×60+20×69=1,500+1,380=2,880=45×6425 \times 60 + 20 \times 69 = 1{,}500 + 1{,}380 = 2{,}880 = 45 \times 64.

Concept
Alligation applied to averages to split a group
Typical time
60 s
Your time
—
The rule this testsThe alligation rule
Practise this chapter →

Ten questions from Mixtures & Alligation, at your own pace.

Practise this chapter →

Ten questions from Mixtures & Alligation, at your own pace.