Simple Interest 1/4

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25. A sum of Rs.2540 is lent out into two parts, one at 12% and another one at $12\displaystyle\frac{1}{2}$%. If the total annual income is Rs.311.60, the money lent at 12% is:
a. Rs.1180
b. Rs.1360
c. Rs.1240
d. Rs.1340

Answer: A

Explanation:
Let money lent at 12% = Rs.x
Then, money lent at $12\displaystyle\frac{1}{2}\% $ = Rs.(2540-x)
$\displaystyle\frac{{x \times 12 \times 1}}{{100}} + (2540 - x) \times \displaystyle\frac{{25}}{2} \times \displaystyle\frac{1}{{100}} = 311.60$
or $\displaystyle\frac{{3x}}{{25}} + \displaystyle\frac{{2540 - x}}{8} = 311.60$
or 24x + 25 (2540 - x) = $200 \times 311.60$
x=63500-62320=1180

26. A money lender finds that due to a fall in the rate of interest from 13% to $12\displaystyle\frac{1}{2}$%, his yearly income diminishes by Rs.104. His capital is :
a. Rs.21400
b. Rs.20800
c. Rs.22300
d. Rs.24000

Answer: B

Explanation:
Let capital = Rs. x. Then,
$\left( {\displaystyle\frac{{x \times 13 \times 1}}{{100}}} \right) - \left( {x \times \displaystyle\frac{{25}}{2} \times \displaystyle\frac{1}{{100}}} \right) = 104$
or ${\displaystyle\frac{{13x}}{{100}} - \displaystyle\frac{x}{8} = 104}$ or 26x-25x
= $104 \times 200$
or x = 20800
Capital = Rs.20800

27. A sum of money amounts to Rs.850 in 3 years and Rs.925 in 4 years. The sum is :
a. Rs.600
b. Rs.575
c. Rs.625
d. Data inadequate

Answer: C

Explanation:
S.I for 1 year = Rs.(925-850)= Rs.75
S.I for 2 years = Rs.$(75 \times 3)$=Rs.225
Sum = Rs.(850-225)=Rs.625

28. The simple interest on a certain sum for 3 years at 14% per annum is Rs.235.20. The sum is :
a. Rs.480
b. Rs.560
c. Rs.650
d. Rs.720

Answer: B

Explanation:
Sum = Rs.$\left( {\displaystyle\frac{{100 \times 235.20}}{{3 \times 14}}} \right) = Rs.560$

29. Rs.2189 are divided into three parts such that their amounts after 1, 2 and 3 years respectively may be equal, the rate of simple interest being 4% p.a.in all cases. The smallest part is :
a. Rs.702
b. Rs.398
c. Rs.756
d. Rs.1093

Answer: B

Explanation:
(Here there is slight problem I think. Instead of amounts it should be interests)
Let the three parts be, p, q ,r. Now interests on these three parts are
$\dfrac{{p \times 1 \times 4}}{{100}}$ = $\dfrac{{q \times 2 \times 4}}{{100}}$ = $\dfrac{{r \times 3 \times 4}}{{100}}$
$ \Rightarrow 4p = 8q = 12r$ $ \Rightarrow$ p = 2q = 3r
Let the above values are equal to $k$
Then $p = k$, $q = \dfrac{k}{2}$, $r = \dfrac{k}{3}$
$p:q:r = 6:3:2$
Smallest part = r = $\dfrac{2}{{6 + 3 + 2}} \times 2189 = 398$

Modification:
Suppose if the question really means amounts, then we have to equal the amounts after the respective years.
$p + \dfrac{{p \times 1 \times 4}}{{100}}$ = $q + \dfrac{{q \times 2 \times 4}}{{100}}$ = $r + \dfrac{{r \times 3 \times 4}}{{100}}$
Now 26p = 27q = 28r
p : q : r = $\dfrac{1}{{26}}:\dfrac{1}{{27}}:\dfrac{1}{{28}}$
Smallest part = $\dfrac{{\dfrac{1}{{28}}}}{{\dfrac{1}{{26}} + \dfrac{1}{{27}} + \dfrac{1}{{28}}}} \times 2189$ = $702\dfrac{{1053}}{{1093}} = 702.96$

30. A man lends Rs.10000 in four parts. If he gets 8% on Rs.2000; $7\displaystyle\frac{1}{2}$% on Rs.4000 and $8\displaystyle\frac{1}{2}$% on Rs.1400, what percent must he get for the remainder, if his average annual interest is 8.13% ?
a. $10\displaystyle\frac{1}{2}$%
b. $9\displaystyle\frac{1}{4}$%
c. 9%
d. 7%

Answer: C

Explanation:
$\left[ {\displaystyle\frac{{2000 \times 8 \times 1}}{{100}}} \right] + \left[ {4000 \times \displaystyle\frac{{15}}{2} \times \displaystyle\frac{1}{{100}}} \right]$ + $\left[ {1400 \times \displaystyle\frac{{17}}{2} \times \displaystyle\frac{1}{{100}}} \right] + \left[ {2600 \times R \times \displaystyle\frac{1}{{100}}} \right]$
= $\displaystyle\frac{{8.13}}{{100}} \times 10000 = \frac{{813}}{{10000}} \times 10000$
$ \Rightarrow 160 + 300 + 119 + 26{\rm{ R = 813}} \Rightarrow {\rm{R = 9}}$

31. A man invests an amount of Rs.15860 in the names of his three sons A,B and C in such a way that they get the same amount after 2,3 and 4 years respectively. If the rate of simple interest is 5%, then the ratio of amounts invested among A,B and C will be:
a. 10 : 15 : 20
b. 22 : 23 : 24
c. 6 : 4 : 3
d. 2 : 3 : 4

Answer: C

Explanation:
The amounts invested be p,q, r respectively
Then, $\displaystyle\frac{{p \times 2 \times 5}}{{100}} = \displaystyle\frac{{q \times 3 \times 5}}{{100}} = \displaystyle\frac{{r \times 4 \times 5}}{{100}} = x$
p = 10x; q = $\displaystyle\frac{{20}}{3}x$; r = 5x
p: q : r = 10x : $\displaystyle\frac{{20}}{3}x$ : 5x = 6 : 4 : 3

32. A man invested $\displaystyle\frac{1}{3}$ of his capital at 7%, $\displaystyle\frac{1}{4}$ at 8% and the remainder at 10%. If his annual income is Rs.561, the capital is :
a. Rs.5400
b. Rs.6000
c. Rs.6600
d. Rs.7200

Answer: C

Explanation:
Let the total capital be "C", then
$\left( {\displaystyle\frac{C}{3} \times \displaystyle\frac{7}{{100}} \times 1} \right) + \left( {\displaystyle\frac{C}{4} \times \displaystyle\frac{8}{{100}} \times 1} \right)$ + $\left( {\displaystyle\frac{{5C}}{{12}} \times \displaystyle\frac{{10}}{{100}} \times 1} \right) = 561$
$ \Rightarrow \displaystyle\frac{{7C}}{{100}} + \displaystyle\frac{C}{{50}} + \displaystyle\frac{C}{{24}} = 561$
$ \Rightarrow 5C = (561 \times 600)$ or C = 6600

33. What should be the least number of years in which the simple interest on R.2600 at $6\displaystyle\frac{2}{3}$% will be an exact number of rupees ?
a. 2
b. 3
c. 4
d. 5

Answer: B

Explanation:
Simple interest = Rs. $\left( {2600 \times \displaystyle\frac{{20}}{3} \times \displaystyle\frac{1}{{100}} \times T} \right)$
= Rs. $\left( {\displaystyle\frac{{520}}{3} \times T} \right)$
To make exact number of rupees, the value of T should be "3" so as to get Rs.520.

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Simple Interest: Formulas Simple Interest: Exercise Simple Interest: Installments