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29 Sep 2025, 21:20
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A
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Difficulty:
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Question Stats:
77% (02:16) correct
23%
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wrong
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A shopkeeper sold 10 items, all of which are of the same cost price, such that profit percentage on no two item is the same. The profits made on the given items were in an arithmetic progression. If the profit percentage of the item the selling price of which is 4th highest and the item the selling price of which is 7th highest were 13% and 10% respectively, what is the profit percentage on the whole?
A. 11.5%
B. 12%
C. 12.5%
D. 13%
E. 13.5%
A. 11.5%
B. 12%
C. 12.5%
D. 13%
E. 13.5%
29 Sep 2025, 22:44
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4th highest gives 13% profit and 7th highest gives 10%, you can see that they're already making an increasing AP
in terms of profit percentage. So we can let our CP = 100 so that absolute values of the profit should make an AP
Total CP = 1000, Total SP = 1115
Total profit percentage = (115/1000) * 100 = 11.5%
GMAT-Club-Forum-yxlwknad.png [ 5.41 KiB | Viewed 747 times ]
in terms of profit percentage. So we can let our CP = 100 so that absolute values of the profit should make an AP
Total CP = 1000, Total SP = 1115
Total profit percentage = (115/1000) * 100 = 11.5%
Bunuel
Attachment:
GMAT-Club-Forum-yxlwknad.png [ 5.41 KiB | Viewed 747 times ]
30 Sep 2025, 09:26
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All items have the same cost price, so ordering by the selling price is same as ordering by the profit percentage.
P1, P2, P3, .......P10 and P4=13% and P7=10%
The common difference between P4 & P7 is 3r [(P5-P4),(P6-P5),(P7-P6)]
P7-P4=13%-10%
3r=3%
r=1%
P1= P4+3r=13%+3%=16%
And P10=P7-3r =10%-3%=7%
P1 to P10 = 16%, 15%, 14%, 13%, 12%, 11%, 10%, 9%, 8%, 7%
Profit percentage on whole= Average of P1 to P10 = (16%+7%)/2 =11.5%
A
P1, P2, P3, .......P10 and P4=13% and P7=10%
The common difference between P4 & P7 is 3r [(P5-P4),(P6-P5),(P7-P6)]
P7-P4=13%-10%
3r=3%
r=1%
P1= P4+3r=13%+3%=16%
And P10=P7-3r =10%-3%=7%
P1 to P10 = 16%, 15%, 14%, 13%, 12%, 11%, 10%, 9%, 8%, 7%
Profit percentage on whole= Average of P1 to P10 = (16%+7%)/2 =11.5%
A
