Crampete

#### 1)What will be the simple interest earned on an amount of Rs.17600 in 9 months at the rate of 4$${1 \over {2}}$$% per annum?

Show Solution
SI =  $${PNR \over {100}}$$

=    $${17600*({3 \over {4}})*({9 \over {2}}) \over {100}}$$ = Rs.594 .  Hence (a).

#### 2)A sum of money at simple interest amounts to Rs.876 in 3 years and to Rs.918 in 4 years. Find the principal.

Show Solution
SI for 1 st year = (918 – 876) = Rs.42

SI for 3 years = 42 * 3 = Rs.126

Principal = (876 – 126 ) = Rs.750   Hence (b).

#### 3)A sum of money becomes 5 times its value under 8 years. In how many years will it become 17times itself?

Show Solution
If a sum becomes 5 times itself in 8 years , the interest will be 4 times that sum.

For the sum to become 17 times itself, the interest has to become 16 times the sum.

SI for n consecutive years follows AP. It will take (8 * 4) = 32 years.    Hence (d).

#### 4)A man borrows Rs.40000 from a bank at 8% per annum. Find the amount after for 3$${1 \over {2}}$$ years

Show Solution
SI =  $${PNR \over {100}}$$
= $${ 40000*({7 \over {2}})* 8 \over {100}}$$ = Rs.11200

Amount = P + SI = 40000 + 11200 = Rs.51200 .   Hence (c).

#### 5)The difference between the simple and compound interest after 2 years at 7% per annum is Rs.98. What is the simple interest after 4 years at the same interest?

Show Solution
Difference between SI and CI after 2 years = Rs.98 =  $${PR{}{}{}{}{}{}{}{}{}{}{}{} \over {100}}$$

P = Rs.20000

SI after 4 years at 7% per annum SI = $${ 20000*4* 7 \over {100}}$$ = Rs.5600 .  Hence (b).

#### 6)The simple interest for 2 years is Rs.4200 and the compound interest for the second year is Rs.2415 for the same principal at the same rate. Find the principal amount.

Show Solution

SI for 2 years = Rs.4200 SI for 1 year = Rs.2100 = PR …..(i) CI for 2nd year = Rs.2415 = PR + PR2 => PR2 = 2415 – 2100 à Rs.315 …..(ii) Divide equation ii and i R = $${315 \over {2100}}$$ à R = 15% Substitute R value in equation i P * $${15 \over {100}}$$ = 2100 = Rs.14000. Hence (c).

#### 7)The ratio of compound interest to simple interest on a certain sum at 16% per annum for 2 years is:

Show Solution

SI = $${PNR \over {100}}$$ = $${P*2*16 \over {100}}$$ = 0.32P CI = P [(1+ $${R \over {100}}$$ ) n - 1] = P [(1+ $${16 \over {100}}$$ ) 2 - 1] = 0.3456P Ratio of CI to SI = $${0.3456P \over {0.32P}}$$ = 27: 25 Hence (b).

#### 8)A invested an amount of Rs.15200 divided in two different banks A and B at the simple interest rate of 16% p.a. and 10% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs.3424, what was the amount invested in bank B?

Show Solution

Let the invested amount in bank A and B be x and 15200-x respectively. SI for 2 years at 16% p.a. = $${x*2*16 \over {100}}$$ = $${32x \over {100}}$$ SI for 2 years at 10% p.a. = $${(15200-x)*2*10 \over {100}}$$ = $${(15200-x)*20 \over {100}}$$ Total SI earned in 2 years = Rs.3424 $${32x \over {100}}$$ + $${(15200-x)*20 \over {100}}$$ = 3424 à x = Rs.3200 Amount invested in bank B = 15200 – x = 15200 – 3200 = Rs.12000 Hence (c).

#### 9)Thedifference between the simple interest and the compound interest for a certain sum after 3 years is Rs.2736 at 4% per annum. Find the principal.

Show Solution
CI – SI = Rs.2736 (after 3 years)

Difference between SI and CI after 3 years = PR 3 + 3PR 2 = Rs.2736

R = 4%

P =  $${2736*100*100*100 \over {R+300R}}$$

= $${2736*100*100*100 \over {16(300+4)}}$$ = Rs.562500 .  Hence (d).

#### 10)Divide Rs.5046 between P and Q such that P’s share at the end of 11 years is equal to Q’s share at the end of 13 years at 5% rate of compound interest. Find the share of P.

Show Solution

Let the shares of P and Q be Rs.x and Rs.y respectively.

Both P and Q get the same amount

x *(1 +  $${5 \over {100}})$$ 11 =  y *(1 +  $${5 \over {100}})$$ 13

$${x \over {y}}$$   =  (1 +  $${5 \over {100}})$$ 2

=  $${441 \over {400}}$$

Share of P =   $${441 \over {841}}$$ * 5046 = Rs.2646   Hence (a).

#### 11)A sum of money was lent at 4% per annum simple interest. After a year, Rs.8400 is repaid and the rest is financed at 8% per annum. If the second year’s interest is $${46 \over {125}}$$ of the first year’s interest, find the sum of money that was lent out.

Show Solution
Let the sum of money lent out be Rs.x
SI for 1 st year =  $${PNR \over {100}}$$ =  $${x*4 \over {100}}$$ =  $${x \over {25}}$$
Amount = x +  $${x \over {25}}$$ =  $${26x \over {25}}$$
Returned amount after first year = Rs.8400
Balance amount = ( $${26x \over {25}}$$ – 8400)
Second year’s interest =   ( ( $${26x \over {25}}$$ – 8400) * 8)/100 =  $${46 \over {125}}$$ of the first year’s interest
(( $${26x \over {25}}$$ – 8400) * 8)/100 =  $${46 \over {125}}$$ *  $${x \over {25}}$$ = Rs.12500 .  Hence (d).

#### 12)Rs.5720 is divided into three parts such that their interest after 1, 2 and 3 years respectively are equal, the rate of interest being 12% per annum in all cases. Find the difference between largest two parts and smallest two parts.

Show Solution

Let a, b and c be the 3 parts invested for 1, 2 and 3 years respectively. Let the interest be d $${a*1*12 \over {100}}$$ = $${b*2*12 \over {100}}$$ = $${c*3*12 \over {100}}$$ = d a = $${25d \over {3}}$$, b = $${25d \over {6}}$$, c = $${25d \over {9}}$$ a: b: c = $${25d \over {3}}$$: $${25d \over {6}}$$: $${25d \over {9}}$$ a: b: c = 6: 3: 2 => 5720 6x + 3x + 2x = 5720 à x = 520 Largest two parts are 6x and 3x. and smallest two parts are 3x and 2x. Difference between largest and smallest two parts = 9x – 5x = 4x = 4*520 = Rs.2080. Hence (c).

#### 13)What will be the interest earned on an amount of Rs.50000 in 2 years at the rate of 10% per annum, if it is compounded half-yearly for the first year and then annually for the second year?

Show Solution
CI is compounded half yearly = p((1+ $${r \over {200}}$$ ) 2n – 1)

Amount   after the first year = 50000(1+ $${10 \over {200}})$$ 2 = Rs.55125

Amount after second year = 55125 (1+  $${10 \over {100}}$$ ) = Rs.60637.5

Total interest = 60637.5 – 50000 = Rs.10637. 5 .  Hence (a).

#### 14)A bought an Air-cooler Rs.7800. he would pay back in two equal instalments. If the rate of interest be 6% per annum compounded annually, find the amount of each instalment.

Show Solution
Let the instalment be Rs.x

Amount at the end of 1 st year = 7800 *  $${106 \over {100}}$$

x = $${7800 \over {{1 \over {1+({6 \over {100}})}}+{1 \over {1+({6 \over {100}})}}}}$$ = Rs.4255.32 .  Hence (b).

#### 15) A man took a loan of Rs.45000 at 9% simple interest for 2 years and deposited it at 8% compound interest for the same period. What was the gain/loss?

Show Solution
SI for 2 years =  $${45000*2*9 \over {100}}$$ =  Rs.8100

Amount he has to return = 45000 + 8100 = Rs.53100

He invested Rs.45000 at 8% CI

Amount = 45000(1+$${8 \over {100}}$$ ) 2 = Rs.52488

Loss = 53100 – 52488 = Rs.612   Hence (d).