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,
1P.W. = (100 x Amount) / (100 + (R x T)) = (100 x T.D.)/ (R x T)
1T.D. = (P.W. x R x T) / 100 = (Amount x R x T) / (100 + (R x T))
1Sum = (S.I. x T.D.) / (S.I. - T.D.)
1S.I. - T.D. = S.I. on T.D.
1When the sum is put at compound interest, then P.W. = Amount/ (1+R/100)T
Solved Examples
Answer - B
Explanation
1P.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
1P.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
1T.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
1P.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
1P.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
1P.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
1T.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
1Amount = 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
1T.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
1S.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
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