Number System - Discounts
Suppose a man has to pay Rs. 156 after 4 years and the rate of interest is 14% per annum. Clearly, Rs. 100 at 14% will amount to R. 156 in 4 years. So, the payment of Rs. now will clear off the debt of Rs. 156 due 4 years hence. We say that:
Sum due = Rs. 156 due 4 years hence;
Present Worth (P.W.) = Rs. 100;
True Discount (T.D.) = Rs. (156 - 100) = Rs. 56 = (Sum due) - (P.W.)
We define: T.D. = Interest on Present Worth;Amount = Present Worth + True Discount
Interest is reckoned on P.W. and true discount is reckoned on the amount.
Important Formulae
Let rate = R% per annum and Time = T years. Then,
P.W. = (100 x Amount) / (100 + (R x T)) = (100 x T.D.)/ (R x T)
T.D. = (P.W. x R x T) / 100 = (Amount x R x T) / (100 + (R x T))
Sum = (S.I. x T.D.) / (S.I. - T.D.)
S.I. - T.D. = S.I. on T.D.
When the sum is put at compound interest, then P.W. = Amount/ (1+R/100)T
Solved Examples
Answer - B
Explanation
P.W.= ((100 x Amount))/(100+(R x T)) = Rs {(100 x 9920)/(100 (3 x 8))} = Rs (100 x 9920)/124 = Rs 8000 Q 2 - The genuine rebate on a bill due 9 months consequently at 6% for each annum is Rs. 180. Discover its present worth.
Answer - A
Explanation
P.W. = ((100 x T.D.))/((R x T)) = Rs {(100 x 180)/(6 x 3/4)} = Rs 4000 Q 3 - The genuine markdown on a sure total of cash due 3 years consequently is Rs 200 and the straightforward enthusiasm on the some aggregate for the same time and at the same guideline is Rs. 240. Discover the aggregate and the rate percent.
Answer - A
Explanation
T.D = Rs 200 and S.I. = Rs 240 Sum due = (S .I. x T.D.)/(S.I.-T.D.) = Rs ((240 x 200))/((240-200)) = Rs 1200
Q 4 - The genuine rebate on Rs 1860 due after a sure time at 5% p.a. is Rs. 60. Discover the time after which it is expected.
Answer - B
Explanation
P.W. = (Amount)-(T.D.) = Rs (1860-60) = Rs 1800 T.D. is S.I. on P.W. Rs. 60 is S.I. on Rs 1800 at 5% p.a. Time = ((100 x 60))/((5 x 1800)) years = 2/3 years = 2/3 x 12 months = 8 months
Q 5 - Find the rebate on Rs. 9920 due 3 years at 8% p.a.
Answer - C
Explanation
P.W.= ((100 x Amount))/(100+(R x T)) = Rs {(100 x 9920)/(100 (3 x 8))} = Rs (100 x 9920)/124 = Rs 8000 T.D. = (Amount)-(P.W.) = Rs (9920-8000) = Rs 1920 Q 6 - The genuine rebate on a bill due 9 months consequently at 6% for each annum is Rs. 180. Discover the charge's measure.
Answer - A
Explanation
P.W. = ((100 x T.D.))/((R x T)) = Rs {(100 x 180)/(6 x 3/4)} = Rs 4000 Sum = (P.W.+T.D.) = Rs (4000+180) = Rs 4180 Q 7 - The genuine markdown on a sure total of cash due 3 years consequently is Rs 200 and the straightforward enthusiasm on the some aggregate for the same time and at the same guideline is Rs. 240. Discover the rate percent.
Answer - D
Explanation
T.D = Rs 200 and S.I. = Rs 240 Sum due = (S .I. x T.D.)/(S.I.-T.D.) = Rs ((240 x 200))/((240-200)) = Rs 1200 T.D is S.I. on the sum. Rs. 240 is S.I. on Rs 1200 for a long time. R= ((100 x 240))/((1200 x 3))% p.a. = 20/3% p.a
Q 8 - The genuine markdown on Rs 2575 due 4 months thus is Rs. 75. Discover the rate of hobby.
Answer - D
Explanation
Amount = Rs 2575, T=4/12 years = 1/3 years, T.D = Rs. 75 P.W. = (Amount) - (T.D.) = Rs (2575-75) = 2500. T.D. Is S.I. on P.W. R.s 75 is S.I. on Rs. 2500 or 1/3 years Rate = ((100x75)/(2500x1/3))% p.a. = 9% p.a.
Q 9 - The genuine rebate on a bill due 10 months consequently at 6% p.a. is Rs 26.25. Discover the charge's measure.
Answer - B
Explanation
T.D. = Rs 26.25, T = 10/12 year= 5/6 year,R=6% p.a. Let P.W. be Rs x. Then, S.I. on Rs x at 6% p.a. for 5/6 year is Rs. 26.25 ∴ (x * 6 * 5/6)/100 = 25.25 => x= (26.25 * 20) = 525 ∴ (P.W.) + (T.D.) = Rs. (525+26.25) = Rs 551.25
Q 10 - The contrast between the S.I. what's more, T.D. on a sure whole of cash for 6 months at 6% p.a. is Rs. 27. Discover the total.
Answer - B
Explanation
S.I. = Rs. (x * 6 * 1/2)/100 = Rs. 3x/100 and T.D. = Rs {(x * 78/12)/(100+(6 * 6/12) )} = Rs. 3x/103 ∴ 3x/100-3x/103 = 27 => (309x-300x) = (27 * 100 * 103) => x = ((27*100*103))/9 = 30900