Higher January 2021 Paper 2 Q10

10 The people working for a company work in Team A or in Team B.

number of people in Team A : number of people in Team B = \(3 : 4\)

\(\dfrac{4}{5}\) of Team A work full time.

24% of Team B work full time.

Work out what fraction of the people working for the company work full time.
Give your fraction in its simplest form.

(3)

Mark scheme

Scheme	Marks
eg \(\dfrac{4}{5} \times \dfrac{3}{7}\left(= \dfrac{12}{35}\right)\) oe or \(0.24 \times \dfrac{4}{7}\left(= \dfrac{96}{700}\right)\) oe or eg \(\dfrac{4}{5} \times 3\left(= \dfrac{12}{5} = 2.4\right)\) and \(0.24 \times 4\left(= \dfrac{24}{25} = 0.96\right)\) (or 3.36) or eg \(\dfrac{4}{5} \times 300\) (= 240) and \(0.24 \times 400\) (= 96) (or 336)	M1
eg \(\text{“}\dfrac{12}{35}\text{”} + \text{“}\dfrac{96}{700}\text{”}\left(= \dfrac{336}{700}\right)\) oe or \(\dfrac{\text{“}2.4\text{”} + \text{“}0.96\text{”}}{3 + 4}\left(= \dfrac{3.36}{7}\right)\) oe or eg \(\dfrac{\text{“}240\text{”} + \text{“}96\text{”}}{300 + 400}\left(= \dfrac{336}{700}\right)\) oe	M1
Correct answer scores full marks (unless from obvious incorrect working) Answer: \(\dfrac{12}{25}\)	A1
	(3)
	(3 marks)

M1: or 0.48 or 48% or correct unsimplified fraction eg \(\dfrac{84}{175}\)

A1: cao