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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?

ARs. 7.19

BRs. 10.40

CRs. 12.07

DRs. 16

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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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$$\frac{1}{2}$$%?

A1200

B3000

C3600

D1300

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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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 :

AThere is no gain or loss to any one

BA gains Rs. 7.34

CA loses Rs. 7.34

DA gains Rs. 11

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

ARs. 1166

BRs. 1360

CRs. 1927

DRs. 1764

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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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 ?

ARs. 28.50

BRs. 37.50

CRs. 5.0

DRs. 50

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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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.

A1500

B1600

C6200

D6000

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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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.

ARs.1175

BRs.1375

CRs.1475

DRs.1575

Explanation:

Here is no explanation for this answer

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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.

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

B(5+ $$\frac{2}{3}$$)%

C(2+ $$\frac{2}{3}$$)%

D(4+ $$\frac{2}{3}$$)%

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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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 :

ARs. 320

BRs. 180

CRs. 160

DNone of these

Explanation:

Here is no explanation for this answer

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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:

A0%

B5%

C7.50%

D10%

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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