find a single discount as percent equevalent to sucessive discount of 10%and 20% i need step by step answer
Answers
Answer:
Here, we will first assume any number of which will find the two successive discounts. So, we will assume that number to be 100. Thus, successive discounts i.e. 20% and 10% on 100 is 72. Thus, the answer is 28%.
(i) Successive discount = 20% and 12%
Let M.P. = ₹ 100
First discount = 20%
Second discount = 12%
∴ S.P. = (M.P. (100 – Discount %)) /100
= (100 × (100 – 20) (100 – 12))/100 × 100
= (100 × 80 × 88)/100 × 100 = 352/5
∴ Total discount on ₹100 = 100 – 352/5
= (500 – 352)/5 = ₹ 148/5
∴ Single discount = 148/5 % = 29. 3/5%
(ii) Successive discount 10%, 20% and 20%
Let M.P. = ₹ 100
∴ S.P. after 3 discounts
= (100(100 – 10) (100 – 20) (100 – 20))/(100 × 100 × 100)
= (100 × 90 × 80 × 80)/(100 × 100 × 100) = 576/10
∴ Total discount = ₹100 – 576/10
= ₹ (1000 – 576)/10 = 424/10
∴ Single discount = 424/10 % = 42.4%
(iii) Successive discounts = 20%, 10%, 5%,
Let M.P. = ₹100
∴ S.P. after three discounts
= ₹ (100(100 – 20)(100 – 10) (100 -5))/(100 × 100 × 100)
= ₹ (100 × 80 × 90 × 95)/(100 × 100 × 100) = ₹342/5
∴ Total discount = 100 – 342/5
= (500 – 342)/5 = 158/5
∴ Single discount = 158/5% = 31.6%