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Jack's monthly remuneration includes a fixed salary and a fixed comm

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Jack's monthly remuneration includes a fixed salary and a fixed comm  [#permalink]

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New post 11 Sep 2017, 09:22
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Jack's monthly remuneration includes a fixed salary and a fixed commission per consignment sold. This commission reduces by x% per consignment after the first 50 by another x% (on the 51-100 commission rate) after the first 100 consignments. In January, the remuneration was $4000 on sale of 30 consignments; in February, the remuneration was $6000 on sale of 50 consignments; in March, the remuneration was $7200 on sale of 70 consignments. If, in April, Jack sold 120 consignments, what shall be his remuneration?

A. $13000
B. $11400
C. $10200
D. $9720
E. $9400

Source : Experts Global

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Re: Jack's monthly remuneration includes a fixed salary and a fixed comm  [#permalink]

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New post 12 Sep 2017, 03:01
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Let base salary = b
initial commission per consignment =c
Reduction in commission after 50 consignment =x%

As given : remuneration = base salary + No.of consignment * c

For January : 4000 = b+30 *c
For February : 6000 = b+50 *c

By solving above 2 equations we get b= 1000 and c=100
So we got base salary value and commission value.

Now suppose after x% reduction commission becomes c1

For March :7200 = b+50*c +20*c1
7200 =1000 +50 *100+20*c1
c1 =60
So after x% reduction commission becomes 60 => (1-x/100) * 100 = 60 => x= 40%
So there is 40% of reduction in commission amount.

SO now after 100 consignments the commission again reduced by x% ie 40%.
So for consignment more than 100 communion amount = (1-x/100)*60 = (1-40/100)*60 = 36 =c2

So April remuneration = b+50*c+50*c1+20*c2
= 1000+50*100+50*60+20*36
=9720

Answer: D
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Re: Jack's monthly remuneration includes a fixed salary and a fixed comm  [#permalink]

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New post 14 Sep 2017, 10:01
Good work, Nikkb

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Re: Jack's monthly remuneration includes a fixed salary and a fixed comm  [#permalink]

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New post 14 Sep 2017, 23:17
pushpitkc wrote:
Jack's monthly remuneration includes a fixed salary and a fixed commission per consignment sold. This commission reduces by x% per consignment after the first 50 by another x% (on the 51-100 commission rate) after the first 100 consignments. In January, the remuneration was $4000 on sale of 30 consignments; in February, the remuneration was $6000 on sale of 50 consignments; in March, the remuneration was $7200 on sale of 70 consignments. If, in April, Jack sold 120 consignments, what shall be his remuneration?

A. $13000
B. $11400
C. $10200
D. $9720
E. $9400

Source : Experts Global

Month - Total Comp - Total Numbers sold
Jan - 4000 - 30
Feb - 6000 - 50
Mar - 7200 - 70
Apr - ???? - 120

Commission % percentage Slabs
Full Commission - 1 to 50
X% reduction - 51 to 100
X% further reduction - 101 onwards

Fix component is common/constant in all months. So, the increase is happening only because of commission.
Jan - 4000 - 30
Feb - 6000 - 50
Total Comp. difference 2000
Total Consign. difference 20
Per Consignment commission = 100

so, Jan Commission is 30*3 = 3000
Jan Total = 4000 So, fixed component is 1000.

Again

Jan - 4000 - 30 = 1000 + 3000 (upto 50)
Feb - 6000 - 50 = 1000 + 5000 (up to 50)
Mar - 7200 - 70 = 1000 + 5000 (up to 50) + 1200 (50 to 100)

In March, 20 additional consignments is earning only 1200. Means per consignment he earns 60.
So, X is 40% reduction from 100 to 60.

now for April
1000 + (50*100) (100 upto 50) + (50*60) (60 per consignment for 51 to 100) + (20 * 36) (40% reduction on 101 to 120)
Total = 9720

D
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Re: Jack's monthly remuneration includes a fixed salary and a fixed comm  [#permalink]

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New post 14 Sep 2017, 23:36
pushpitkc wrote:
Jack's monthly remuneration includes a fixed salary and a fixed commission per consignment sold. This commission reduces by x% per consignment after the first 50 by another x% (on the 51-100 commission rate) after the first 100 consignments. In January, the remuneration was $4000 on sale of 30 consignments; in February, the remuneration was $6000 on sale of 50 consignments; in March, the remuneration was $7200 on sale of 70 consignments. If, in April, Jack sold 120 consignments, what shall be his remuneration?

A. $13000
B. $11400
C. $10200
D. $9720
E. $9400

Source : Experts Global

For 30 consignments, his salary is $4000 and for 50 consignments, his salary is $6000. So, for 20 additional consignments, he earned $2000.

This shows his fixed salary is $1000 and commission per assignment is $100.

Now, for 70 consignments, he earned $7200 but must have been $8000 [$1000 (fixed salary) and $100*70 =$7000] but he earns a total of only $7200.

Having said that, it means he loses $800 per 20 extra (70 - 50) consignments he added to his list. This equals $40 per consignment. So, the commission he gets post 50 and below 100 is $60. A reduction of 40% which is x%.
His next slab's commission will be 60% of $60 which is $36.


Now, for 120 consignments, his total earnings will be sum of $1000 (his fixed salary), $100*50 (consignments from 1 to 50), $ 60*50 (consignments from 51 to 100) and $36*20 (consignments from 101 to 120). It totals to be $1000 + $5000 + $3000 + $720 = $9720.

The Variable : I change but remain constant ;)
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Re: Jack's monthly remuneration includes a fixed salary and a fixed comm  [#permalink]

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New post 17 Sep 2017, 22:30
salary= Fixed Salary (FS) + Fixed compensation (FC)

4000=FS + FC*30
6000= FS+ FC*50
Solving both the equations
FC=100
now put FC in either of the equation to find FS
4000=FS+ 100*30
so,FS=1000

now 7200=FS+FC*50+ 20* reduced value of FC (let it be a)
solving the above equation we get a=60
Now here is the trick don't get confused 100-60= 40 $ so you have to reduced 40 dollars in the FC for conignments above 100.It is mentioned that there is an x% decrease.So find out percent decrease (100-60)/100*100= 40% decrease now x is 40 .
salary for 120 consignments= FS+FC*50+FC(x% decreased value that is 40%)*50+FC(two times decreased value by 40% which is .6*60 )*20
salary= 1000+50*100+50*60+20*36=9720
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Re: Jack's monthly remuneration includes a fixed salary and a fixed comm  [#permalink]

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New post 04 Nov 2018, 00:27
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Re: Jack's monthly remuneration includes a fixed salary and a fixed comm &nbs [#permalink] 04 Nov 2018, 00:27
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