In September, Liam gave his wife, Barbara, $4000 for household expenditure. Barbara spent 50% of the sum on rental, 30% on food and saved the rest. In October, Liam reduced the sum he gave to Barbara. Barbara spent the same amount on rental and reduced the amount she spent on food by 20%. She saved the remaining 20% of the sum given to her in October. By what percentage was the sum given to Barbara reduced by?

	Rental	Food	Savings	Total
Before	50%	30%	20%	$4000
Change		- 6%	- ?	- ?
After	50%	24%
Comparing the amounts spent in October	80 u		20 u	100 u

Amount that Liam saved in percent
= 100% - 50% - 30%
= 20%

Amount that Liam reduced on food in percent
= 20% x 30%
= ²⁰₁₀₀ x 30
= 6%

Total amount that Liam spent on rental and food in percent
= 50% + 24%
= 74%

100% → 4000

1% → 4000 ÷ 100 = 40

74% → 74 x  40 = 2960

The total amount that Liam spent on rental and food is repeated. 

80 u = 74% 

80 u = 2960

1 u = 2960 ÷ 80 = 37

Amount that Liam gave to Barbara in October
= 100 u
= 100 x 37
= $3700

Amount that Barbara received less from Liam from September to October
= 4000 - 3700
= $300

Percentage that the sum given to Barbara was reduced by from September to October
= ³⁰⁰₄₀₀₀ x 100%
= 7.5%

Answer(s): 7.5%