The price of a product increased by 3.5% in the last year

Question

The price of a product increased by 3.5% in the last year, with the price consisting of raw materials and taxes. If the cost of raw materials increased by 3% and the tax increased by 5.5%, what percentage of the product's costs did the taxes costs represent at the beginning of the year?

A) 0.15
B) 0.55
C) 0.35
D) 0.2
E) 0.27

A) 0.15
B) 0.55
C) 0.35
D) 0.2
E) 0.27

sss2503 · Answer

Let proportion of tax be x, so proportion of raw material cost is 1-x. Then, by increment ratios given,

0.03(1-x) + 0.055x = 0.035
0.025x = 0.005
x = 0.2

Archit3110 · Answer

1.03x+1.055y=1.035x+1.035y
4y=x

y/(5y) =.2
Option D

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Kinshook · Answer

@jjsettaGiven: The price of a product increased by 3.5% in the last year, with the price consisting of raw materials and taxes.
Asked: If the cost of raw materials increased by 3% and the tax increased by 5.5%, what percentage of the product's costs did the taxes costs represent at the beginning of the year?
Let the raw material cost be r & taxes be t at the beginning of the year.

Original price of product = r+t
Increased price of product = 1.035(r+t)

Increased price of raw materials = 1.03r
Increased taxes = 1.055t

1.035(r+t) = 1.03r + 1.055t
.005r = .02t
t/r = .005/.02 = .25
t/(r+t) = .25/1.25 = .2 = 20%

The percentage of the product's costs did the taxes costs represent at the beginning of the year = t/(r+t) = 20%

​​​​​​​IMO D

arushi118 · Answer

In the beginning:
let raw mat = x
tax = y

after increase:
raw mat = 1.03x
tax = 1.055y

/(x+y) = 3.5/100
on solving:
x = 4y

we have to find -> y/(x+y) = 0.2
D is correct.

vasu1104 · Answer

say price of raw material = M
price of tax= P
price of product= 100x

so M + P =100x

new price of raw material = 1.03M
new price of tax= 1.055P
new price of product= 103.5x
1.03M + 1.055P = 103.5x

we need to find p / 100x
so now we have two unknowns, lets find p

from eq 1, M= 100x- P

put this into eq 2
1.03(100x-P) + 1.055P = 103.5x
103x- 1.03p + 1.055p = 103.5x
0.20P = 0.5x
p = 20x

so 20x / 100x
0.2
option D

The price of a product increased by 3.5% in the last year

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The price of a product increased by 3.5% in the last year

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