Arithmetic Aptitude :: True Discount

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Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?

Explanation:

S.I. on Rs. (260 - 20) for a given time = Rs. 20.
S.I. on Rs. 240 for half the time = Rs. 10.
T.D. on Rs. 250 = Rs. 10.
T.D. on Rs. 260 = Rs. $$\frac{10}{250} * 260$$ = Rs. 10.40

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2 / 25

A bill falls due in 1 year.The creditor agrees to accept immediate payment of the half and to defer the payment of the other half for 2 years.By this arrangement ins Rs.40.what is the amount of the bill,if he money be worth 12$$\frac{1}{2}$$%?

Explanation:

Let the sum be Rs. x. Then,
$$\left[\frac{x}{2} + \frac{ \frac{x}{2} * 100}{100 + \left( \frac{25}{2} * 2\right)} \right] - \frac{x * 100}{100 + \left(\frac{25}{2} * 1 \right)}$$ = 40
or, $$\frac{x}{2} + \frac{2x}{5} - \frac{8x}{9}$$ = 40
or, x = Rs. 3600.
Therefore, amount of the bill = Rs. 3600.

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3 / 25

A has to pay Rs. 220 to B after 1 year. B asks A to pay Rs. 110 in cash and defer the payment of Rs. 110 for 2 years. A agrees to it. If the rate of interest be 10% per annum, in this mode of payment :

Explanation:

Amount of money that A has to pay = P.W of Rs. 220 due 1 year hence

= Rs. $$\frac{220 * 100}{\left[ 100 + \left(10 * 1 \right)\right]}$$

= Rs. 200

Amount of money A actually pays = Rs. 110 + P.W of Rs. 110 due 2 years hence

= $$\frac{110 + \left( 110 * 100 \right)}{100 + \left(10 * 2\right)}$$

= Rs. 192.66

Therefore, A gains = Rs. ( 200 - 192.66 )

= Rs. 7.34

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4 / 25

The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is:

Explanation:

Let, P.W be Rs. x.

Then, S.I on Rs. x at 16% for 9 months = Rs. 189

So, x * 16 * $$\left(\frac{ 9}{12}\right)$$ * $$\left(\frac{ 1 }{ 100 }\right)$$ = 189

or, x= Rs. 1575

Therefore, Amount due = P.W + T.D

= Rs. ( 1575 + 189 )

= Rs. 1764

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5 / 25

A owes B, Rs. 1573 payable 1$$\frac{1}{2}$$ years hence. Also B owes A, Rs.1444.50 payable 6 months hence. If they want to settle the account forthwith, keeping 14% as the rate of interest, then who should pay and how much ?

Explanation:

A owes = P.w of Rs. 1573 due 3/2 years hence

= Rs. $$\left[\frac{1573 * 100 }{100 + 14 * \left(\frac{3}{2}\right)}\right]$$

= Rs. ( 1573 x 100 ) / 121

= Rs. 1300

B owes = P.W of Rs. 1444.50 due 6 months hence

= Rs. $$\left[\frac{1444.50 * 100}{100 + 14 * \left(\frac{ 1}{2}\right)}\right]$$

= Rs. $$\left(\frac{1444.50 * 100}{ 107}\right)$$

= Rs. 1350

Therefore, B should pay Rs. ( 1350 - 1300 ) = Rs. 50, to A.

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6 / 25

The true discount on a bill due 9 months hence at 12% per annum is Rs. Find the amount of the bill and its present worth.

Explanation:

Let the amount of the bill be Rs. a

Then,

$$\left[\frac{a * r * t}{ 100 + ( r * t )}\right]$$ = T.D

or, $$\left[\frac{a * 12 * \frac{3}{4} } {100 + ( 12 * \frac{3}{4})}\right]$$ = 540

or, a = 540*$$\frac{109}{9}$$

or, a = Rs. 6540

Therefore, Amount = Rs. 6540

Hence, Present worth, P.W = Rs. ( 6540 - 540 )

= Rs. 6000

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7 / 25

The present value of a bill due at the end of 2 years is Rs.1250. If the bill were due at the end of 2 years and 11 months, its present worth would be Rs.1200. Find the rate of interest and the sum.

Explanation:

Here is no explanation for this answer

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8 / 25

The true discount on a certain sum of money due 3 year hence is Rs.100 and the S.I. on the same sum for the same time and at the same rate is Rs.120. Find the sum and the rate percent.

Explanation:

Sum can be calculated as,

S = $$\frac{S.I * T.D }{S.I - T.D}$$

= Rs. $$\left[\frac{120 * 100}{120 - 100}\right]$$

= Rs. 600

And, Rate = $$\left[\frac{100 * 120 }{ 600 x 3}\right]$$

= 6.667%

= (6 + $$\frac{2}{3}$$) %

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9 / 25

Suppose Rajendra 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 Rs. 156 in 4 years. So, the payment of Rs. 100 now will clear off the debt of Rs.156 due 4 years. Hence, we say that :

Explanation:

Here is no explanation for this answer

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10 / 25

A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of:

Explanation:

Given,

Cost price, C.P = Rs. 3000

Now, S.P can be calculated as, S.P = Rs. $$\left[\frac{3600 * 100}{ 100 + (10 * 2 )}\right]$$

= Rs. 3000
Since S.P is equal to C.P.
Therefore, Gain = 0%.

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