Aptitude::True Discount
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Example 1 / 8
P.W. = \(\frac{100 \times Amount}{100 + (R \times T)}\) = Rs\([\frac{100 \times 930}{100 + (8 \times 3)}]\) = Rs. \(\frac{100 \times 930}{124}\) = Rs. 750.
T.D. = (Amount) – (P.W.) = Rs. (930 -750) = Rs. 180.Ans.
T.D. = (Amount) – (P.W.) = Rs. (930 -750) = Rs. 180.Ans.
NA
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Example 2 / 8
P.W. = \(\frac{100 \times T.D.}{R \times T}\) = \(\frac{100 \times 168}{14 \times 2}\) = 600
Sum =(P.W. +T.D.) = Rs. (600 +168) = Rs.768 Ans.
Sum =(P.W. +T.D.) = Rs. (600 +168) = Rs.768 Ans.
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Example 3 / 8
Let amount be Rs. x.
Then, interest on (P.W) Rs. x at 16% for 9 months = Rs. 189.
=> \(\frac{x \times 16 \times \frac{9}{12}}{100 + \left(16 \times \frac{9}{12}\right)}\) = 189
=> \(\frac{x \times 16 \times \frac{3}{4}}{100 + \left(16 \times \frac{3}{4}\right)}\) = 189
=> \(\frac{x \times 12}{100 + 12}\) = 189
=> x = \(\frac{189 \times 112}{12}\)
=> x (Amount) = Rs. 1764.
=> P.W. = Rs. \(\left(1764 - 189\right)\) = Rs. 1575.Ans.
Then, interest on (P.W) Rs. x at 16% for 9 months = Rs. 189.
=> \(\frac{x \times 16 \times \frac{9}{12}}{100 + \left(16 \times \frac{9}{12}\right)}\) = 189
=> \(\frac{x \times 16 \times \frac{3}{4}}{100 + \left(16 \times \frac{3}{4}\right)}\) = 189
=> \(\frac{x \times 12}{100 + 12}\) = 189
=> x = \(\frac{189 \times 112}{12}\)
=> x (Amount) = Rs. 1764.
=> P.W. = Rs. \(\left(1764 - 189\right)\) = Rs. 1575.Ans.
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Example 4 / 8
P.W. = \(\frac{100 \times T.D.}{R \times T}\) = \(\frac{100 \times 168}{14 \times 2}\) = 600.
Sum =(P.W. +T.D.) = Rs. (600 +168) = Rs. 768.
Sum =(P.W. +T.D.) = Rs. (600 +168) = Rs. 768.
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Example 5 / 8
S.I on Rs. (110 -10) for a certain time = Rs. 10.
S.I. on Rs. 100 for double the time = Rs. 20.
T.D. on Rs. 120 = Rs. (120 -100) = Rs. 20.
T.D. on Rs. 110 = Rs. (\(\frac{20}{120}\) x 110) = Rs. 18.33.Ans.
NA
NA
NA
Example 6 / 8
Given, T.D.(True Discount) = Rs. 250 and S.I.(Simple Interest) = Rs. 375.
Sum due = \(\frac{S.I. \times T.D}{(S.I.) – (T.D.)}\)
= Rs. \(\left(\frac{375 \times 250}{375 – 250}\right)\) = Rs. 750.
Rate = \(\left(\frac{100 \times 375}{750 \times 3}\right)\)% = 16\(\frac{2}{3}\)%
Sum due = \(\frac{S.I. \times T.D}{(S.I.) – (T.D.)}\)
= Rs. \(\left(\frac{375 \times 250}{375 – 250}\right)\) = Rs. 750.
Rate = \(\left(\frac{100 \times 375}{750 \times 3}\right)\)% = 16\(\frac{2}{3}\)%
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Example 7 / 8
Given,
Time = 6 months =\(\frac{1}{2}\) of year.
Rate = 12\(\frac{1}{2}\)% = \(\frac{25}{2}\)%
Consider,
True discount = \(\frac{A * R * T}{100 + (R * T)}\)
⇒ True discount = \(\frac{x * \frac{25}{2} * \frac{1}{2}}{100 + (\frac{25}{2} * \frac{1}{2})}\)
⇒ True discount = \(x * \frac{25}{4} * \frac{4}{425}\)
⇒ True discount = \(\frac{25x}{425}\)
⇒ True discount = \(\frac{x}{17}\)
Now,
Simple interest = (\(x * \frac{25}{2} * \frac{1}{2} * \frac{1}{100})\)
⇒ Simple interest = \(\frac{x}{16}\)
Therefore,
\(\frac{x}{16}\) – \(\frac{x}{17}\) = 30.
⇒ 17\(x\) – 16\(x\) = 30 * 16 * 17
⇒ \(x\) = 8160
Therefore, sum due = Rs. 8160.Ans.
Time = 6 months =\(\frac{1}{2}\) of year.
Rate = 12\(\frac{1}{2}\)% = \(\frac{25}{2}\)%
Consider,
True discount = \(\frac{A * R * T}{100 + (R * T)}\)
⇒ True discount = \(\frac{x * \frac{25}{2} * \frac{1}{2}}{100 + (\frac{25}{2} * \frac{1}{2})}\)
⇒ True discount = \(x * \frac{25}{4} * \frac{4}{425}\)
⇒ True discount = \(\frac{25x}{425}\)
⇒ True discount = \(\frac{x}{17}\)
Now,
Simple interest = (\(x * \frac{25}{2} * \frac{1}{2} * \frac{1}{100})\)
⇒ Simple interest = \(\frac{x}{16}\)
Therefore,
\(\frac{x}{16}\) – \(\frac{x}{17}\) = 30.
⇒ 17\(x\) – 16\(x\) = 30 * 16 * 17
⇒ \(x\) = 8160
Therefore, sum due = Rs. 8160.Ans.
NA
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NA
Example 8 / 8
Let the sum be \(x\). Then,
⇒ \(\left[ \frac{x}{2} + \frac {\frac{x}{2} * 100} {100 + (\frac{25}{2} * 2)} \right] \)– \(\frac{x * 100}{100 + (\frac{25}{2} * 1)}\) = 50.
⇒ \(\frac{x}{2} + \frac{2x}{5} – \frac{8x}{9}\) = 50.
⇒ \(\frac{45x + 36x – 80x}{90}\) = 50
⇒ \(\frac{x}{90}\) = 50
⇒ \(x\) = 4500.
Therefore, amount of the bill = Rs. 4500.Ans.
⇒ \(\left[ \frac{x}{2} + \frac {\frac{x}{2} * 100} {100 + (\frac{25}{2} * 2)} \right] \)– \(\frac{x * 100}{100 + (\frac{25}{2} * 1)}\) = 50.
⇒ \(\frac{x}{2} + \frac{2x}{5} – \frac{8x}{9}\) = 50.
⇒ \(\frac{45x + 36x – 80x}{90}\) = 50
⇒ \(\frac{x}{90}\) = 50
⇒ \(x\) = 4500.
Therefore, amount of the bill = Rs. 4500.Ans.
NA
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NA