The present worth of Rs. 1320 due 2 years hence at 10% per annum is:
Answer: B
Correct answer: Rs. 1100
\[PW = \frac{A \times 100}{100 + RT} = \frac{1320 \times 100}{100 + 20} = \frac{132000}{120} = 1100\]
Checking: the simple interest on Rs. 1100 for 2 years at 10% is Rs. 220, and \(1100 + 220 = 1320\).
Please log in or register to report this question.
There was 25% off on handbags. Madhu bought a handbag. She also got a 10% discount for paying cash. She paid Rs. 405. What as the price tag on the handbag?
Answer: D
Both discounts apply in turn to the price tag, so work backwards from what she paid.
\[ \text{MP} \times 0.75 \times 0.90 = 405 \]
\[ \text{MP} \times 0.675 = 405 \quad\Longrightarrow\quad \text{MP} = \frac{405}{0.675} = \text{Rs. } 600 \]
Checking forwards: \( 600 \times 0.75 = 450 \), and \( 450 \times 0.90 = 405 \). Rs. 450 appears as a distractor because it is the price after the first discount only.
Please log in or register to report this question.
The present worth of a bill of Rs. 2650 due 9 months hence at 8% per annum is:
Answer: A
Correct answer: Rs. 2500
With \(RT = 8 \times \tfrac{3}{4} = 6\):
\[PW = \frac{2650 \times 100}{106} = 2500\]
The true discount is the remaining Rs. 150, which is nine months of interest on Rs. 2500 at 8%.
Please log in or register to report this question.
The True discount on Rs1760 due after a certain time at 12% per annum is Rs160. The time after which it is due is?
Answer: D
\[ \text{PW} = 1760 - 160 = \text{Rs. } 1600 \]
\[ 160 = \frac{1600 \times 12 \times T}{100} = 192\,T \]
\[ T = \frac{160}{192} = \frac{5}{6} \text{ year} = 10 \text{ months} \]
The interest runs on the Rs. 1600 present worth, not the Rs. 1760 face value; using the latter would give about 9 months.
Please log in or register to report this question.
The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 25 and Rs. 20 respectively. What is the sum ?
Answer: A
Correct answer: Rs. 100
Simple interest is reckoned on the amount and true discount on the present worth, and the standard relation between them is
\[\text{Sum} = \frac{SI \times TD}{SI - TD} = \frac{25 \times 20}{25 - 20} = \frac{500}{5} = 100\]
The gap between the two figures is exactly the interest on the true discount itself.
Please log in or register to report this question.
The present worth of Rs. 1404 due in two equal half-yearly installments at 8% per annum simple interest is:
Answer: A
Two equal half-yearly installments of Rs. 702 each - one due in 6 months, the other in 12 - must be discounted separately for their own waiting times.
\[ \text{PW}_{1} = \frac{702}{1 + \dfrac{8 \times 0.5}{100}} = \frac{702}{1.04} = \text{Rs. } 675 \]
\[ \text{PW}_{2} = \frac{702}{1 + \dfrac{8 \times 1}{100}} = \frac{702}{1.08} = \text{Rs. } 650 \]
\[ \text{total} = 675 + 650 = \text{Rs. } 1325 \]
Discounting the whole Rs. 1404 for a single averaged period does not give the same answer, because discounting is not linear in time.
Please log in or register to report this question.
The interest on Rs. 750 for 2 years is the same as the true discount on Rs. 960 due 2 years hence. If the rate of interest is the same in both cases, it is:
Answer: C
Write \( k = \dfrac{R \times 2}{100} \) for the rate–time product over the two years. Simple interest is charged on the full sum, true discount on the present worth:
\[ \text{SI} = 750\,k, \qquad \text{TD} = \frac{960\,k}{1+k} \]
Setting them equal and cancelling \( k \):
\[ 750(1+k) = 960 \quad\Longrightarrow\quad 1 + k = 1.28 \quad\Longrightarrow\quad k = 0.28 \]
\[ \frac{2R}{100} = 0.28 \quad\Longrightarrow\quad R = 14\% \]
Cancelling \( k \) from both sides is what makes the problem solvable in one line; the two years then divide out at the very end.
Please log in or register to report this question.
The difference between Simple Interest and True Discount on a certain sum of money for 6 months at 12 1/2% per annum is Rs 25. Find the sum.
Answer: A
Simple interest is charged on the amount and true discount on the present worth, so with \( k = \dfrac{RT}{100} \):
\[ \text{SI} - \text{TD} = A\,k - \frac{A\,k}{1+k} = \frac{A\,k^{2}}{1+k} \]
Here \( T = 0.5 \) year at \( 12\tfrac{1}{2}\% \):
\[ k = \frac{12.5 \times 0.5}{100} = 0.0625 \]
\[ 25 = \frac{A \times 0.0625^{2}}{1.0625} = \frac{A \times 0.00390625}{1.0625} \]
\[ A = \frac{25 \times 1.0625}{0.00390625} = \text{Rs. } 6800 \]
The gap between simple interest and true discount is itself the banker's gain, which is why it depends on \( k^{2} \) and stays small for short periods.
Please log in or register to report this question.
Gurpreet went to a shop and bought a sofa, on which she got a 20% discount. Had she been given a 25% discount she would have saved Rs. 1000 more. What was the marked price of the sofa?
Answer: C
The extra saving comes from the extra 5 percentage points of discount, and that difference is measured on the marked price.
\[ (25\% - 20\%) \times \text{MP} = 1000 \]
\[ 0.05 \times \text{MP} = 1000 \quad\Longrightarrow\quad \text{MP} = \frac{1000}{0.05} = \text{Rs. } 20{,}000 \]
As a check, a 20% discount leaves Rs. 16,000 and a 25% discount leaves Rs. 15,000 - a difference of exactly Rs. 1000. Only the gap between the two discount rates matters, never either rate on its own.
Please log in or register to report this question.
If the true discount on s sum due 2 years hence at 14% per annum be Rs. 168, the sum due is ?
Answer: C
True discount is simple interest on the present worth, so find that first.
\[ k = \frac{14 \times 2}{100} = 0.28 \]
\[ \text{PW} = \frac{\text{TD}}{k} = \frac{168}{0.28} = \text{Rs. } 600 \]
\[ \text{sum due} = 600 + 168 = \text{Rs. } 768 \]
The division gives only the present worth; the discount still has to be added back to reach the sum due.
Please log in or register to report this question.
