If $ 10 be allowed as true discount on a bill of $ 110 due at the end of certain time, then the discount allowed on the same amount due at the end of double the time is :

Let the marked price = ? N
The discount equivalent to successive discounts 20 % and 10 % = { r₁ + r₂ - (r₁ r₂)/100 } %
Where, r₁ = 20 and r₂ = 10
Then, 30 - 2 = 28 %
According to the question,
{(100 - 28)N}/100 - {(100 - 30)N}/100 = 72
? (72N - 70N)/100 = 72
? N = (72 x 100)/2 = ? 3600

Let the CP of book = ? P
Then, SP of book = {(100 + 12) x P}/100 = 112P/100
Now, the printed price = ? Q
Then, after discount,
the SP = (100 - 10)Q/100 = 90Q/100
Since, both SP are same.
Then, 112P/100 = 90Q/100
? P/Q = 45/56
? 45 : 56

? Marked price of an article = ? 50
? SP of an article = 50 x (100 - 20)/100
= (50 x 80)/100
= ? 40

Hence, cost price of an article = (40 x 100)/(100 + 25)
= (40 x 100)/125
= ? 32

Let CP of the goods = ? N
? Marked price of the goods = N x {(100 + 30)/100} = ? 13N/10

Now, SP of the goods = (13N/10) x (100 - 15/100)
= (13N/10) x (85/100) = ? 221N/200

? Profit = {(221 x N)/200} - N = ? 21N/200

Hence, profit per cent = [{21N/200} /N] x 100 % = 2100/200 = 10.5 %

Let MP of an article = ? R
? SP of an article = ? 3R/4
and CP of an article
= (3R/4) x {100/(100 + 25)}
= 3R/4 x (100/125)
= ? 3R/5
Required ratio = R : 3R/5 = 5 : 3