Higher June 2024 Paper 1 Q14

14 The combined savings of Abel and Bahira are 15 435 dinars.

The savings of Bahira are 45% more than the savings of Abel.

The savings of Bahira are \(\dfrac{3}{2}\) times the savings of Chanda.

Work out the savings of Chanda.

(5)

Mark scheme

Scheme	Marks
1 + 1.45 (= 2.45) or \(1 + \dfrac{29}{20}\left(= \dfrac{49}{20}\right)\) or B = 1.45A oe or \(\text{B} = \dfrac{29}{20}\text{A}\) oe or A + 1.45A or \(\text{A} + \dfrac{29}{20}\text{A}\) or 2.45A or (A : B =) 100 : 145 oe or 100 + 145 (= 245) oe or (B : C =) 3 : 2 oe or \(B = 1.5C\) oe	B1
A + 1.45A = 15 435 or 15 435 ÷ “2.45” or 15 435 ÷ \(\text{``}{\dfrac{49}{20}}\text{''}\) or 15 435 ÷ “245” × 100 or 63 × 100 (= 6300)	M1
15 435 – “6300” or 1.45 × “6300” or 145 × “63” (= 9135) or M2 (for this mark and the one above) for \(15\,435 \div \left(\dfrac{1}{1.45} + 1\right)\) (= 9135) oe or \(15\,435 \div \left(\dfrac{49}{29}\right)\) (= 9135) oe	M1
“9135” ÷ \(\dfrac{3}{2}\) oe or “9135” × \(\dfrac{2}{3}\) oe	M1
Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: 6090	A1
	(5)
	(5 marks)

B1: must identify ratios with Abel and Bahira or Bahira and Chanda

Allow any letters for A, B and C

M1: for a method to find Abel’s savings
or
for 6300

M1: for a method to find Bahira’s savings
or
for 9135

M1: for a method to find to find Chanda’s savings