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# Over the last three years a scientist had an average (arithmetic mean)

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Over the last three years a scientist had an average (arithmetic mean)  [#permalink]

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01 Dec 2018, 08:07
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45% (medium)

Question Stats:

60% (01:51) correct 40% (02:04) wrong based on 68 sessions

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Over the last three years a scientist had an average (arithmetic mean) yearly income of $45,000. The scientist earned $$1\frac{1}{2}$$ times as much the second year as the first year and $$2\frac{1}{2}$$ times as much the third year as the first year. What was the scientist's income the second year? (A)$9,000
(B) $13,500 (e)$27,000
(D) $40,500 (E)$45,000

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Re: Over the last three years a scientist had an average (arithmetic mean)  [#permalink]

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01 Dec 2018, 08:25
1
Average of 3 years = 45,000$Total income in 3 years = 135,000$

Let the income in first year be x.
Now, x+3/2x+5/x = 135,000
x = 27,000$Income in second year = 1.5(27000) = 40,500$

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Re: Over the last three years a scientist had an average (arithmetic mean)  [#permalink]

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01 Dec 2018, 15:21
1
Let first year salary be x
then second year salary = 1.5x
Third year = 2.5 x
Average salary for three years is 45000 which means total salary for 3 years = 45000(3)
x+1.5x+2.5x=135000
5x=135000
x=27000

Second year salary is 1.5x= 1.5*27000
=$40,500 D is the correct answer VP Joined: 09 Mar 2016 Posts: 1286 Over the last three years a scientist had an average (arithmetic mean) [#permalink] ### Show Tags 02 Dec 2018, 03:00 Average income for three months is 45000, then total income for three months is 45,000*3 = 135,000 "The scientist earned $$1\frac{1}{2}$$ times as much the second year as the first year" So, Let First year be $$x$$ Then second Year is $$\frac{3x}{2}$$ "and $$2\frac{1}{2}$$ times as much the third year as the first year" So third Year is $$\frac{5x}{2}$$ $$\frac{X}{1} +\frac{3x}{2}+\frac{5x}{2} = 135,000$$ $$\frac{10x}{2}$$ = $$135,000$$ $$10x = 270,000$$ $$x = 27,000$$ Second year = $$\frac{3}{2} * 27000 = 40,500$$ Director Joined: 09 Mar 2018 Posts: 933 Location: India Re: Over the last three years a scientist had an average (arithmetic mean) [#permalink] ### Show Tags 10 Feb 2019, 20:09 HKD1710 wrote: Over the last three years a scientist had an average (arithmetic mean) yearly income of$45,000. The scientist earned $$1\frac{1}{2}$$ times as much the second year as the first year and $$2\frac{1}{2}$$ times as much the third year as the first year. What was the scientist's income the second year?

(A) $9,000 (B)$13,500
(e) $27,000 (D)$40,500
(E) \$45,000

3 Years AM = 45000, Total Sum will be 135000

Given Y2 = 3/2 Y1
Y3 = 5/2 Y1

Y1 + Y2 + Y3 = 135000
substitute for above
Y1 = 27000

Y2 = 3/2 Y1 = 40500

D
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Re: Over the last three years a scientist had an average (arithmetic mean)   [#permalink] 10 Feb 2019, 20:09
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