the selling price of a cake in a shop was reduced by 12% during a Christmas sale.on account of new year,the pricewa further reducedby12.5%.what is the total discount percentage from the original price of the cake?
Answers
Answer:
23%
Step-by-step explanation:
Initially 12% of 100 =88%.
Then after discount of 12.5 you need to reduce it from 88 and not from 100.
So, 12.5 % of 88 =11
(12.5/100*88= 12.5/50*44=12.5/25*22=1/2*22=22/2=11)
Hence the total percentage reduced =12%+11%=23%
- The total discount percentage from the original price of the cake is equal to 23% .
Given :-
- Selling price of cake reduced by, during christmas sale = 12%
- Selling price of cake further reduced by, during new year sale = 12.5%
To Find :-
- Total discount % ?
Solution (1) :- Basic Method
Let us assume that, original selling price of the cake was Rs. 100x
So,
→ Original selling price of cake = Rs. 100x
→ Selling price reduced by ( during christmas ) = 12% of original selling price = 12% of 100x = (12 × 100x)/100 = Rs. 12x
then,
→ New price of cake during christmas = Original selling price - reduced price = 100x - 12x = Rs. 88x
now,
→ New selling price of cake during christmas = Rs. 88x
→ Selling price reduced by ( during new year ) = 12.5% of selling price during christmas = 12.5% of 88x = (12.5 × 88x)/100 = Rs. 11x
then,
→ New price of cake during new year = selling price of cake during christmas - reduced price = 88x - 11x = Rs. 77x
therefore,
→ Total discount = Original selling price - New price of cake during new year
→ Total discount = 100x - 77x
→ Total discount = Rs. 23x
hence,
→ Total discount % = (Total discount in Rs. × 100) / Original selling price
→ Total discount % = (23x × 100) / 100x
→ Total discount % = 23% (Ans.)
Solution (2) :- Direct formula
Let first discount is equal to D1 % and further discount is D2 % then,
- Total discount % = (-1)(D1 + D2) + {(D1 × D2)/100}
given that,
- D1 = 12%
- D2 = 12.5%
putting values of D1 and D2 in above told formula we get,
→ Total discount % = (-1)(D1 + D2) + {(D1 × D2)/100}
→ Total discount % = (-1)(12 + 12.5) + {(12 × 12.5)/100}
→ Total discount % = (-1)•24.5 + (150/100)
→ Total discount % = (-24.5) + 1.5
→ Total discount % = (-23) %
{ Here -ve sign shows that, discount is given or original price is reduced. }
Hence, total discount percentage is equal to 23% .
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