In September, Cole gave his wife, Lucy, $6000 for household expenditure. Lucy spent 60% of the sum on rental, 30% on food and saved the rest. In October, Cole reduced the sum he gave to Lucy. Lucy spent the same amount on rental and reduced the amount she spent on food by 30%. She saved the remaining 10% of the sum given to her in October. By what percentage was the sum given to Lucy reduced by?

	Rental	Food	Savings	Total
Before	60%	30%	10%	$6000
Change		- 9%	- ?	- ?
After	60%	21%
Comparing the amounts spent in October	90 u		10 u	100 u

Amount that Cole saved in percent
= 100% - 60% - 30%
= 10%

Amount that Cole reduced on food in percent
= 30% x 30%
= ³⁰₁₀₀ x 30
= 9%

Total amount that Cole spent on rental and food in percent
= 60% + 21%
= 81%

100% → 6000

1% → 6000 ÷ 100 = 60

81% → 81 x  60 = 4860

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

90 u = 81% 

90 u = 4860

1 u = 4860 ÷ 90 = 54

Amount that Cole gave to Lucy in October
= 100 u
= 100 x 54
= $5400

Amount that Lucy received less from Cole from September to October
= 6000 - 5400
= $600

Percentage that the sum given to Lucy was reduced by from September to October
= ⁶⁰⁰₆₀₀₀ x 100%
= 10%

Answer(s): 10%