A survey reveals that the average income of a company’s customers is $

Question

A survey reveals that the average income of a company’s customers is $45,000 per year. If 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is $75,000, what is the average income of the other 40 customers?

(A) $27,500
(B) $35,000
(C) $37,500
(D) $42,500
(E) $50,000

(A) $27,500
(B) $35,000
(C) $37,500
(D) $42,500
(E) $50,000

Is there a way to solve this using weighted average concept instead of doing tedious calculations?

gurpreetsingh · Answer

45*50 = 10*75 + 4x
=> 4x = 2250-750 = 1500
=? x = 375

Hence C

Spidy001 · Answer

let x be the average of 40 customers

40*x + 10* 75000 = 50*45000

solving this we have x= 37500

Answer is C.

Are you sure the official answer is D? if not change please change the answer.

Yalephd · Answer

Awesome. Thank you, Gurpreetsingh and Spidy001.

I selected the wrong OA. The correct answer is C

Spidy001 · Answer

you can even solve this by weighted average. Here is the approach. you can use either one of the above approaches.

(10/50)(75000) + (40/50)*x = (50/50)*45000

=> 750000 + 40x = 45000*50

=> x = 375000

amit2k9 · Answer

total amount of the 40 people =   divided by 40 gives the average.

/40

= 375000.

subhashghosh · Answer

(50*45 - 75 * 10)/40

= (2250 - 750)/40

= 1500/40

= 150/4 * 1000 (multiply by 1000 as 3 zeroes trimmed earlier)

= 37.5 * 100

= 37500

Answer - C

KarishmaB · Answer

Use:
 \frac{w1}{w2} = \frac{(A2 - Avg)}{(Avg - A1)}

\frac{40}{10} = \frac{(75,000 - 45,000)}{(Avg - 30,000)}

Avg - 30,000 = \frac{(30,000)}{4}

Avg = 37,500

PallavTandon · Answer

Total income of all 50 customer = 45,000 * 50 =$2,250,000
Total income of top 10 customers = 75,000 * 10 = $750,000

Total income of rest 40 = 2250000-750000--> $1,500,000

Answer is C

Average income of 40 customers = 1,500,000 / 40 = $37,500

jamifahad · Answer

@Karishma in above formula, u have substituted avg=45000 in numerator but in denominator u haven't substituted same for avg. can i please know how so?

KarishmaB · Answer

That's something I messed up. I actually meant to say:
 \frac{w1}{w2} = \frac{(A2 - Avg)}{(Avg - A1)}

\frac{40}{10} = \frac{(75,000 - 45,000)}{(45,000 - A1)}

45,000 - A1 = \frac{(30,000)}{4}

A1 = 37,500

144144 · Answer

we know that the highest salaries "pulled" the avg
75-45 = 30 for each one. so total of 300 above the avg.

now - to go back down - we need to pull the avg back down (-300) so we need to divide 
-300/40 = -7.5. so the avg of the other 40 will be 45+(-7.5) = 37.5

similar to the weight system of Karishma, but for some reason its easier for me to work by understanding.

stonecold · Answer

Here is my solution to this one =>

Sum(50)=450000*50
Sum(10)=75000*10

Sum(40)= 1500000

Hence Average = 1500000/4 => $37,500

Hence C

JeffTargetTestPrep · Answer

The total income of all customers is 45,000 x 50 = $2,250,000.

The total income of the wealthiest 10 of those customers is 75,000 x 10 = $750,000.

So the total income of the remaining 40 customers is 2,250,000 - 750,000 = $1,500,000 leaving us with an average of:

1,500,000/40 = $37,500

Answer: C

KSBGC · Answer

Total = 50*45000 = 2250000

Total of 10 wealthiest = 10 * 75000 = 750000

Remaining amounts = 2250000 - 750000 = 1500000

1500000 / 40 = 37500

C is the answer.

Archit3110 · Answer

total income sum = 45000*50 ; 2250000
wealthiest income sum = 75000*10 ; 750000
so 40 customers sum = 2250000-750000= 15*10^5
avg 15*10^5/40 = $37,500

IMO C

A survey reveals that the average income of a company’s customers is $

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A survey reveals that the average income of a company’s customers is $

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