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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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11 Sep 2017, 10:22
1
10
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Difficulty:

65% (hard)

Question Stats:

69% (03:29) correct 31% (03:30) wrong based on 91 sessions

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

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12 Sep 2017, 04:01
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1
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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14 Sep 2017, 11:01
Good work, Nikkb

Video Explanation provided by Experts Global

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

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15 Sep 2017, 00:17
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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15 Sep 2017, 00:36
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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17 Sep 2017, 23:30
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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04 Nov 2018, 01:27
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Re: Jack's monthly remuneration includes a fixed salary and a fixed comm   [#permalink] 04 Nov 2018, 01:27
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