A shopkeeper offers the following three schemes:
I. Buy 9 get 1 free
II. Buy 7 get 8
III. Two successive discounts of 20% and 15%
Which scheme has the lowest discount percentage (all articles have the same marked price)?
- AScheme I
- BAll are equal
- CScheme III
- DScheme II
Solution & Step-by-step Explanation
Let the marked price (MP) of each article be ₹10.
Scheme I: Buy 9 get 1 free
Total articles received = 9+1=10⟹Total MP=₹100
Free articles = 1⟹Discount=₹10
Discount %=
100
10
×100%=10%
Scheme II: Buy 7 get 8
This means you pay for 7 articles but get 8 articles.
Total articles received = 8⟹Total MP=₹80
Free articles = 8−7=1⟹Discount=₹10
Discount %=
8
1
×100%=12.5%
Scheme III: Two successive discounts of 20% and 15%
Net discount formula: x+y−
100
xy
Net Discount %=20+15−
100
20×15
=35−3=32%
Comparing the discount percentages:
Scheme I: 10%
Scheme II: 12.5%
Scheme III: 32%
The lowest discount percentage is offered by Scheme I.
Scheme I: Buy 9 get 1 free
Total articles received = 9+1=10⟹Total MP=₹100
Free articles = 1⟹Discount=₹10
Discount %=
100
10
×100%=10%
Scheme II: Buy 7 get 8
This means you pay for 7 articles but get 8 articles.
Total articles received = 8⟹Total MP=₹80
Free articles = 8−7=1⟹Discount=₹10
Discount %=
8
1
×100%=12.5%
Scheme III: Two successive discounts of 20% and 15%
Net discount formula: x+y−
100
xy
Net Discount %=20+15−
100
20×15
=35−3=32%
Comparing the discount percentages:
Scheme I: 10%
Scheme II: 12.5%
Scheme III: 32%
The lowest discount percentage is offered by Scheme I.