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# The price of a radio was increased by 25 percent.

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29 Jun 2014, 22:27
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The price of a radio was increased by 25 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases?

A. 80%
B. 75%
C. 65%
D. 50%
E. 45%

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Re: The price of a radio was increased by 25 percent.  [#permalink]

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29 Jun 2014, 22:52
3

Say initial cost = 100

Increase by 25% = 125

Further increase by 40%$$= 125 * \frac{40}{100} = 50$$

New price = 125 + 50 = 175

Total increase = 75%
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Re: The price of a radio was increased by 25 percent.  [#permalink]

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30 Mar 2016, 14:42
consider base price - $100 25% increase = 1.25*100 =$125
another 40% increase on new price = 1.4* 125 = $175 so final price of radio -$175
therefore a 75% increase

correct option - B
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29 Sep 2016, 23:50
The price of a radio was increased by 25 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases?

A. 80%
B. 75%
C. 65%
D. 50%
E. 45%

Let the initial price of radio be $100 25% of 100 is 25 therefore, with the increase of 25%, the cost of radio becomes$100 + $25 =$125

Now, as mentioned there is also a increase of 40% in the new price ($125) so, find the 40% of$125
40/100 * 125 = $50 Adding this 40% increase ($50) to the new price ($125) will results as -$125 + $50 =$175

Now, as the question says we need to figure out that single increase of percent in the initial amount ($100) which would give us the value we got after the increase of both the percents ($175)
find out what percentage $175 is of$100

Let the unknown percentage be 'x'
$100* 'x'/100 =$175
'x' = 175%

Single Increase in percentage is -
175% - 100% = 75%

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I have tried explaining it this elaborate so that it is easier to understand otherwise this question shouldn't take more than 30-45 seconds.
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Re: The price of a radio was increased by 25 percent.  [#permalink]

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02 Oct 2016, 04:45
Just put in the formula :-
A+B+ A*B/100

40 + 25 + 40*25/100 = 75.

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Re: The price of a radio was increased by 25 percent.  [#permalink]

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27 Feb 2017, 04:08
Let the initial price be 100
After 1st increment, the price will be 1.25*100 =125
After 2nd increment, the price will be 1.4*125 = 175
Net price increment is 75
Percentage is 75% : Option B
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Re: The price of a radio was increased by 25 percent.  [#permalink]

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21 Jun 2017, 04:53
Gnpth wrote:
The price of a radio was increased by 25 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases?

A. 80%
B. 75%
C. 65%
D. 50%
E. 45%

We can apply a few simple formulas to sovle this

x(1.25)
x(1.40) let x be 10 so really just

1.25x1.40 = 1.75

Thus
"B"
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Re: The price of a radio was increased by 25 percent.  [#permalink]

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21 Jun 2017, 07:26
Gnpth wrote:
The price of a radio was increased by 25 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases?

A. 80%
B. 75%
C. 65%
D. 50%
E. 45%

$$+25 + 40 + \frac{(25*40)}{100}$$

= $$65 + 10$$

= $$75$$

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21 Jun 2017, 17:56
Nunuboy1994 wrote:
Gnpth wrote:
The price of a radio was increased by 25 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases?

A. 80%
B. 75%
C. 65%
D. 50%
E. 45%

We can apply a few simple formulas to sovle this

x(1.25)
x(1.40) let x be 10 so really just

1.25x1.40 = 1.75

Thus
"B"

I might be mistaken, but I think you mean let x be 1.

For successive percent changes, if the question asks for overall percent change (and not, e.g., for the new or old price), you can just multiply the multipliers, and if the result is bigger than 1,then subtract 1 . . .IF x = 1 (which it can and does in the product of multipliers method).

As you noted, a 25% increase = 1 + .25 = 1.25

Another 40% increase is 1.40

Multiply the multipliers: (1.25)*(1.4) = 1.75

Overall or "single" percent change is

(1.75 - 1) *100 = .75 *100 = 75%

If x = 10, it looks, from the way it's written, as if you'd subtract 10 from 1.75, leaving -8.25.

Maybe you meant:
10 * 1.75 = 17.5

17.5 - 10 = 7.5

$$\frac{7.5}{10}$$ = .75*100 = 75%

Bottom line is just that if you use 1 as original value, you can simply multiply the multipliers, and if result is greater than 1, then subtract 1 to get percent change / increase in decimal form.

If you use 10, you can multiply that by the product of the multipliers (1.75), and then do $$\frac{change}{original}$$, to get percent change / increase.

You can't, however, just subtract 10 from the multipliers' product in the same way that, using x = 1, you can just subtract 1.
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Re: The price of a radio was increased by 25 percent.  [#permalink]

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21 Jun 2017, 21:37
Start with 100. After first increase, it becomes = 25% more than 100 = 125.

After second increase, it becomes = 40% more than 125 = 140% of 125 = 140/100 * 125 = 175.

We started with 100, ended up at 175. This is equivalent to a single increase of 75%. Hence B answer
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Re: The price of a radio was increased by 25 percent.  [#permalink]

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24 Jun 2017, 08:23
Gnpth wrote:
The price of a radio was increased by 25 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases?

A. 80%
B. 75%
C. 65%
D. 50%
E. 45%

Since the price of the radio was increased by 25% and then by 40%, it was increased by 1.25 x 1.4 = 1.75, or 75%.

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Re: The price of a radio was increased by 25 percent.  [#permalink]

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03 Dec 2018, 11:51
This is a percents question with no specific number given, so it is a good strategy to pick a number. Let's let the original price be 100. The decimal equivalent of 25% is 0.25. So when the original price is increased by 25%, the increase is 0.25(100) = 25. After the 25% increase, the new price is 100 + 25 = 125. Then this price of 125 is increased by 40%. The decimal equivalent of 40% is 0.4. So when the price of 125 is increased by 40%, the increase is 0.4(125) = 50. The final price is 125 + 50 = 175. So the original price was 100 and the final price was 175. This is an increase of . The percent that 75 is of 100 is 75%. A percent increase of 75% is equivalent to the two percent increases. (B) is correct.

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Re: The price of a radio was increased by 25 percent.  [#permalink]

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04 Dec 2018, 09:09
Take it one step at a time:

1) Given a % so use a 100% as your start
2) Increase of 25% so 100 + 25 = 125%
3) 125% increased by 40%,
so i. 10% of 125% = 12.5%
ii. 12.5% * 4 = 50.0%
iii. 125% + 50% = 175%
4) 175%-100%/ 100% = 75%
Re: The price of a radio was increased by 25 percent.   [#permalink] 04 Dec 2018, 09:09
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