find a single discount which is equal to aseries of discount of 10%,12%,15%,20%
Answers
Answer:
Single discount = 46.144%
Step-by-step explanation:
Let "x" be the original marked price
Discounts of 10%, 12%, 15% and 20% are successively applied on "x".
Now, applying a discount of a% means that the article has been sold for (100-a)% of the marked price.
Discount of a% => SP = (100-a)% of MP
&
SP = (100 - a)% of MP => Discount of a%
Thus, if a discount of 10% has been applied on the marked price, the new price is 90% of the marked price. This is same as 0.9 times the marked price.
When the above mentioned discounts are serially applied on "x",
SP = 0.90*0.88*0.85*0.80*MP
= 0.53856*MP
= 53.856% of MP
= (100 - 46.144)% of MP
= 100% of MP - 46.144% of MP
= MP - 46.144% of MP
= MP less (46.144% of MP)
=> Discount = 46.144%
Successive discounts of 10%, 12%, 15% and 20% are equivalent to a single discount of 46.144%.
Verification:
Let marked price (MP) be "x"
A discount of 10% would mean SP = 0.90*x
A successive discount of 12% would mean SP = 0.88*0.90*x
A successive discount of 15% would mean SP = 0.85*0.88*0.90*x
A successive discount of 20% would mean SP = 0.80*0.85*0.88*0.90*x
= 0.53856*x
A single discount of 46.144% on "x", would mean:
SP = x - 46.144% of x
= x - 0.46144*x
= (1 - 0.46144)*x
= 0.53856*x
Thus, verified