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February 26th, 2017, 06:36 PM   #1
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Percentage Word Problem

Retail Division accounts for 40% of Maritime bank’s profit. If the bank wants to grow its overall profit by 15% only through the Retail Division, by how many percentage does this division’s profit have to grow?

The answer given is 37.5% but I have no idea how they got it. Can someone please explain each step?
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February 26th, 2017, 07:36 PM   #2
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Quote:
Originally Posted by jkl46 View Post
Retail Division accounts for 40% of Maritime bank’s profit. If the bank wants to grow its overall profit by 15% only through the Retail Division, by how many percentage does this division’s profit have to grow?

The answer given is 37.5% but I have no idea how they got it. Can someone please explain each step?
let $P_i$ be the bank's initial profit.

$retail = 0.4 P_i$

$other = 0.6 P_i$

They want to increase their profit by 15% to become

$P_f = P_i(1.15) = (1+g)retail + other$

$(1.15)P_i = (1+g) (0.4 P_i) + 0.6 P_i$

$1.15 P_i =( 0.4 (1+g)+0.6) P_i$

$1.15 = 0.4(1+g)+0.6$

$0.55 = 0.4(1+g)$

$1.375 = 1+g$

$g=0.375 = 37.5\%$
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February 27th, 2017, 01:05 AM   #3
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.15/.40 also works.
Since the retail part is only 40%, it must increase by 2.5 times the goal (2.5 * 40% = 100%), which is 2.5 * 15% = 37.5%
1/.4 is 2.5, which is why .15/.4 works.
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