In a sale Tommy bought a kettle and a toaster. He paid a total of $105. The amount paid for the kettle is 2/5 the cost of the toaster. The total price before the discount should have been $133. The toaster was reduced by 20%. How much was the kettle reduced by?
Note:If we reduce a by b%, then final amount will
be = a - ab/100
= a(100-b)/100.
Let the cost of the toaster is $x.
Since the amount paid for the kettle is 2/5 the
cost of the toaster, then the cost of kettle will
be $ 2x/5.
According to the given conditions,
x + 2x/5 = 105
Or, 7x/5 = 105
Or, x = 105*5/7 = 75
So, the cost of the toaster is = $75 and the cost of the kettle is = $(105-75) =$30.
Since the toaster was reduced by 20%, then before reduction its price was
= $ 100*75/(100-20) = $ 93.75
Thus before reduction the price of kettle was = $(133-93.75) = $ 39.25
So, the percentage of reduction of the price of kettle is
= ((39.25 - 30)*100)/30 = 23.5669%
Therefore required answer is 23.5669%.
Let the amount Paid for toaster = x
the amount Paid for Kettle = 2x/5
x + 2x/5 = 105
or (5x - 2x)/5 = 105
7x = 525
x = 75
Cost of Toaster = $75
Cost of Kettle = 2/5 * 75 = $30
Discount on Toaster = 20%
actual discount on toaster
= 20/100 * 75 = $15
Total discount = 133 - 105 = $28
discount on Kettle = 28 - 15 = $13
Kettle was reduced by $13
Let the price of the toaster==T
The price of the kettle ==2/5T
T + 2/5T ==105, solve for T
T ==$75 - price of the toaster after 20%discount.
75 x 2/5==$30 -price of the kettle before 20% discount.
T x 0.80 ==$75, solve for T
T ==75 / 0.8 ==$93.75 - price of the toaster before 20% discount
133 - 93.75 ==$39.25 - price of the kettle before 20% discount.
1 - [30 / 39.25] ==23.567% - discount percentage on the kettle.
Let toaster be Paid = x
Kettle Paid = 2/5x = 2x
Total 7x = 105
x = 15
Kettle Price = 30
and Toaster Price = 75
Before discount Kettle Price 80% x = 30
=> x = 30/80 * 100
x = $37.5
Price of toaster before reduced = $95.5
reduced Price = 20.5/95.5 * 100
Kettle reduced = 21.4%
Total price before the discount -> $193
He paid -> $105
Suppose the price of toaster -> $x
the toaster was reduced 20%
= x * 80/100 = 1/5 = $4x/5
then, price paid of kettle = 4x/5 * 2/5
= $8x/25
according to the clue
4x/5 + 8x/25 = 105
(20x + 8x)/25 = 105
x = 93.75 [Total price of kettle]
reduced price of kettle = 4x/5 = 4 * 93.75/5
= $75
Difference = 93.75 - 75
= $18.75
so, the kettle was reduced by $18.75
