In October, David gave his wife, Yen, $6500 for household expenditure. Yen spent 50% of the sum on rental, 20% on food and saved the rest. In November, David reduced the sum he gave to Yen. Yen spent the same amount on rental and reduced the amount she spent on food by 30%. She saved the remaining 20% of the sum given to her in November. By what percentage was the sum given to Yen reduced by?

	Rental	Food	Savings	Total
Before	50%	20%	30%	$6500
Change		- 6%	- ?	- ?
After	50%	14%
Comparing the amounts spent in November	80 u		20 u	100 u

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

Amount that David reduced on food in percent
= 30% x 20%
= ³⁰₁₀₀ x 20
= 6%

Total amount that David spent on rental and food in percent
= 50% + 14%
= 64%

100% → 6500

1% → 6500 ÷ 100 = 65

64% → 64 x  65 = 4160

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

80 u = 64% 

80 u = 4160

1 u = 4160 ÷ 80 = 52

Amount that David gave to Yen in November
= 100 u
= 100 x 52
= $5200

Amount that Yen received less from David from October to November
= 6500 - 5200
= $1300

Percentage that the sum given to Yen was reduced by from October to November
= ¹³⁰⁰₆₅₀₀ x 100%
= 20%

Answer(s): 20%