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True - Discount
1.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:

Answer:Option 1

Explanation:

Solution:
C.P.=Rs.3000.S.P.=Rs.[3600×100100+(10×2)]=Rs.3000.Gain=0%.

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2.The true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is:

Answer:Option 1

Explanation:

Solution:
P.W.=Rs.(2562122)=Rs.2440S.I.onRs.2440for4monthsisRs.122.Rate=[100×1222440×13]%=15%

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3.A trader owes a merchant Rs. 10,028 due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest 12% per annum, how much cash should he pay?

Answer:Option 1

Explanation:

Solution:
RequiredMoney = P.W.ofRs.10028due9monthshence=Rs.[10028×100100+(12×912)]=Rs.9200.

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4.If Rs. 10 be allowed as true discount on a bill of Rs. 110 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:

Answer:Option 1

Explanation:

Solution:
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.onRs.110=Rs.(20120×110)=Rs.18.33

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5.Goods were bought for Rs. 600 and sold the same for Rs. 688.50 at a credit of 9 months and thus gaining 2% The rate of interest per annum is:

Answer:Option 1

Explanation:

Solution:
S.P.=102%ofRs.600=(102100×600)=Rs.612.Now,P.W. = Rs.612andsum=Rs.688.50.T.D.=Rs.(688.50612)=Rs.76.50.Thus,S.I.onRs.612for9monthsisRs.76.50.Rate=(100×76.50612×34)%=1623%

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

Answer:Option 1

Explanation:

Solution:
LetP.W.beRs.x.Then,S.I.onRs.xat16%for9months=Rs.189.x×16×912×1100=189orx=1575.P.W.=Rs.1575.Sumdue=P.W.+T.D.=Rs.(1575+189)=Rs.1764.

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7.A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man:

Answer:Option 1

Explanation:

Solution:
S.P. = P.W.ofRs.2200due1yearhence=Rs.[2200×100100+(10×1)]=Rs.2000.Gain=Rs.(20001950)=Rs.50.

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8.The present worth of Rs. 2310 due 21/2 years hence, the rate of interest being 15% per annum, is:

Answer:Option 1

Explanation:

Solution:
P.W.=Rs.[100×2310100+(15×52)]=Rs.1680.

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9.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?

Answer:Option 1

Explanation:

Solution:
S.I.onRs.(260 - 20)foragiventime=Rs.20.S.I.onRs.240forhalftime=Rs.10.T.D.onRs.250=Rs.10.T.D.onRs.260=Rs.(10250×260)=Rs.10.40

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10.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:Option 1

Explanation:

Solution:
S.I. on Rs. 750 = T.D. on Rs. 960.
This means P.W. of Rs. 960 due 2 years hence is Rs. 750.
∴ T.D. = Rs. (960 - 750) = Rs. 210.
Thus, S.I. on R.s 750 for 2 years is Rs. 210.
Rate=(100×210750×2)%=14%

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