Question

15. Find a single discount (as percent) equivalent
to following successive discounts:
(i) 20% and 12% (i) 10%, 20% and 20%
(iii) 20%, 10% and 5%​

Answer 1

Find a single discount (as percent) equivalent to following successive discounts: (i) 20% and 12% (ii) 10%, 20% and 20% (iii) 20%, 10% and 5%

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Answer 2

Answer:

(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