Let the amount invested by Amala, Bina and Gouri be 3x, 4x and 5x respectively.&nbsp;Also, let the respective rates be 6r, 5r and 4r.So, the respective ratio of simple interest is (3x × 6r) : (4x × 5r) : (5x × 4r)&nbsp;= 18xr : 20xr : 20xr.Bina's interest income exceeds Amala's by Rs 250.∴ 20xr − 18xr = 250.∴ xr = 125.Total interest income = 18xr + 20xr + 20xr = 58xr = 58 × 125 = Rs. 7250.Hence, option (b).

For a difference of 1 year, CI can be computed as SI.&nbsp;Hence, from the 2nd year to the 3rd year interest earned&nbsp;= (675 – 625) = Rs. 50 on Rs. 625.Hence the Rate of&nbsp;interest&nbsp;50/625&nbsp;× 100 = 8% p.a.Hence, option (b).

Consider the solution for first question of this set.As seen from the table, the total interest&nbsp;collected by Ghosh Babu is Rs.24 on Rs.100.&nbsp;Hence&nbsp;on Rs.50000, it would be 24/100 × Rs. 50,000 = Rs. 12,000Hence, option (a).

Rate of interest is 10% per annum. Hence, interest for half a year is 5%.The Principal, P is invested for 1.5 years or 3 terms of half years.Therefore, P (1 + 5%)3&nbsp;= 18522.⇒ P × 1.053&nbsp;= 18522⇒ P × $$\left( \frac{105}{100} \right)^{3}$$= 18522⇒ P × $$\left( \frac{21}{20} \right)^{3}$$ = 2 × 213⇒ P = 2 × 203&nbsp;= 16000.Hence, 16000.

Ghosh Babu withdrew the maximum amount after the&nbsp;2nd year.Hence, option (b).

Let the Principal be Rs. P.Simple Interest for 3 years = $$\frac{3\ \text{x}\ P\ \text{x}\ 3}{100} = \frac{9P}{100}= 0.09P$$Compound Interest for 2 years = P × 1.052&nbsp;– P = 0.1025P∴ 0.1025P – 0.09P = 1125⇒ 0.0125P = 1125⇒ P = 90,000Hence, 90000.

Consider the solution for first question of this set.He collected the maximum interest after the 1st&nbsp;year.Hence, option (a).

Let the amounts become equal in t years.Veeru’s investment after t years = 10000 $$\left( 1+\frac{5\ \text{x}\ t}{100} \right)$$Joy’s investment after t years = 8000 $$\left( 1+\frac{10\ \text{x}\ \left( t-2 \right)}{100} \right)$$∴ 10000 $$\left( 1+\frac{5\ \text{x}\ t}{100} \right)$$ = 8000 $$\left( 1+\frac{10\ \text{x}\ \left( t-2 \right)}{100} \right)$$⇒ 5 $$\left( 1+\frac{5\ \text{x}\ t}{100} \right)$$ = 4 $$\left( 1+\frac{10\ \text{x}\ \left( t-2 \right)}{100} \right)$$⇒ 500 + 25t = 400 + 40t - 80⇒ t = 12Hence, 12.

Consider the solution for first question of this set.He withdrew the smallest amount after the 4th&nbsp;year.Hence, option (d).

Let Raju invests Rs. A in bank B at r% p.a. for t years.∴ Rupa invests Rs. 10,000 in bank C at 2r% p.a. for 2t years.Total interest accrued for Raju = Art/100This is same as interest accrued by investing same amount in bank A for a year.Amount due after 1 year in bank A = A$$\left[ 1+\frac{3}{100} \right]^{2}$$= 1.0609AInterest accrued = 1.0609A - A = 0.0609A⇒ 0.0609A = $$\frac{Art}{100}$$⇒ rt = 6.09Now, interest accrued by Rupa = $$\frac{10000 \ \text{x}\ 2r\ \text{x}\ 2t}{100}$$ = 400 × rt = 400 × 6.09 = 2436.Hence, option (d).

Let us assume that Ghosh Babu had deposited Rs.100&nbsp;initially.<img alt="" src="https://apti4all.com/storage/photos/1/Past%20Year%20Papers/1991/CAT/ghoshbabu1.jpeg" style="width:303px">Hence, had he deposited Rs.100 initially, he should&nbsp;have withdrawn Rs.22 at the end to close the account.&nbsp;Since he withdrew Rs.11000, at the end, he should&nbsp;have initially deposited = 100/22&nbsp;× 11,000 =&nbsp;Rs.50,000.Hence, option (c).

Let the interest accrued during first year = I and rate of interest be r%We know in case of compound interest, interest for each year increases by r% every year.∴ Interest for 2nd&nbsp;year = I&nbsp;× $$\left( 1+\frac{r}{100} \right)$$= 806.25&nbsp;…(1)Interest for 3rd&nbsp;year = I × $$\left( 1+\frac{r}{100} \right)^{2}$$= 866.72&nbsp;…(2)(2) ÷ (1)⇒ $$\left( 1+\frac{r}{100} \right) = \frac{866.72}{806.25}=1\ - \frac{60.47}{806.25}$$⇒ r = 7.5%∴ Interest for 4th&nbsp;year = Interest for 3rd&nbsp;year × (1+r/100)= 866.72 × $$\left( 1+\frac{7.5}{100} \right)$$ = 931.72Hence, option (c).

Using alligation, the ratio of the amounts invested at both the rates = 2 : 1.Since he has invested Rs.3,000 at 5%, he should further invest Rs.1,500 at 8% to earn a total interest of 6% per annum.<img src="https://apti4all.com/storage/photos/1/Past%20Year%20Papers/1995/QA/66s.png">Alternative method:Let the amount invested at 8% be Rs.&nbsp;x.Then, $$3000\ \text{x}\ \frac{105}{100}\ +\ \text{x}\ \frac{108}{100}=\left( 3000+\ \text{x} \right)\frac{106}{100}3000\ \text{x}\ \frac{105}{100}\ +\ \text{x}\ \frac{108}{100}=\left( 3000+\ \text{x} \right)\frac{106}{100}$$⇒ 0.02x = 30&nbsp;⇒ x = 1,500∴&nbsp;He should further invest Rs.1,500 at 5% to earn a total interest of 6% per annum.

Rs. 8000 is invested at 5.5% earning yearly interest of 8000 × 5.5% = Rs. 440Rs. 5000 is invested at 5.6% earning yearly interest of 5000 × 5.6% = Rs. 280Rs. 7000 is invested at x% earning yearly interest of 7000 × x% = Rs. 70xOverall, 20,000 is invested which earns 5% yearly interest = 5% of 20000 = 1000⇒ 440 + 280 + 70x = 1000⇒ 70x = 1000 – 720 = 280⇒ x = 4%∴ If she had invested her entire initial capital in bank C alone, then her annual interest income = 4% of 20000 = Rs. 800Hence, option (a).

The only difference in the two situations is that in the second situation, Gopal lent Rs. Y more to Ishan than in the first situation. Therefore the additional interest retained by Gopal = 0.1Y.Therefore 0.1.Y = 150 or Y = 1500.Now, Ankit lent Gopal Rs. X at 8% interest. Therefore the interest retained by Ankit = Rs. 0.08X.Gopal lent Ishan Rs. (X + 1500) at 10% interest.Therefore the interest retained by Gopal = 0.1X + 150 - 0.08X = 0.02X + 150Therefore, 0.08X = 0.02X + 1500 or X = 2500.Therefore the value of X + Y = 4000.Hence, 4000.

Let the total investment be Rs. 1500.⇒ Rs. 300 is invested at 6% ⇒ Interest/year = Rs. 18⇒ Rs. 500 is invested at 10% ⇒ Interest/year = Rs. 50⇒ Rs. 700 is invested at 1% ⇒ Interest/year = Rs. 7∴ Total interest received/year = 18 + 50 + 7 = Rs. 75⇒ Time required to receive Rs. 1500 as interest = $$\frac{1500}{75}$$= 20 years.Hence, 20.

Let the part of principal amount in the first instalment be Rs. X.Interest for the first year on Rs. 2,10,0000 = 210000 × 0.1 = 21,000∴ The first instalment = (21000 + X)Remaining part of the principal&nbsp;= (210000 – X)Amount due on this principal of (210000 – X)&nbsp;= (210000 – X) × 1.1 = 231000 – 1.1X∴ The second instalment =&nbsp;231000 – 1.1X∴ 21000 + X = 231000 – 1.1XSolving this, we get X = 1,00,000∴ Each instalment = 100000 + 21000&nbsp;= Rs. 1,21,000Hence, 121000.

Let the amount invested in first and second parts is F and S respectively.$$\Rightarrow \frac{F\ \text{x}\ 15\ \text{x}\ 4}{100} = \frac{S\ \text{x}\ 12\ \text{x}\ 3}{100}$$$$\Rightarrow \frac{F}{S}=\frac{3}{5}$$⇒ % amount invested in first part = $$\frac{3}{3+5}$$ × 100% = 37.5%Hence, option (d).

Let the amount paid at the end of 2nd year be Rs. x.∴ 2,00,000&nbsp;× $$\left( 1+\frac{8/2}{100} \right)^{2\ \text{x}\ 3}$$= 10,320&nbsp;×$$\left( 1+\frac{8/2}{100} \right)^{2\ \text{x}\ 2}$$ + x⇒ 200000&nbsp;× (1.04)6&nbsp;= 10320&nbsp;× (1.04)4&nbsp;+ x⇒ 253063&nbsp;= 12072&nbsp;+ x⇒ x = 240991∴ Total interest paid = (10320 + 240991) - 200000 = 51311Hence, option (d).

The amount on the first investment of Anmol = 12,000 × (1.08) = 12,960So the Interest on this investment is 12,960 - 12,000 = 960.The amount on the second investment of Anmol = 10,000 × (1.03)2&nbsp;= 10,609So the Interest on this investment is 10,609 - 10,000 = 609.So the total interest on these returns = 960 + 609 = 1,569.Bimal has to get this as Simple Interest by investing X rupees at 7.5%That means, X × 0.075 = 1,569X = 20,920So, Bimal has to invest 20,920 rupees.Hence, 20920.

Since the amount invested is in the ratio 2 : 1, we can assum the amout to be 2x and x respectively.∴ Amount invested in fixed deposit = 15L − 3x&nbsp;(where L is lakhs)Simple interest earned on the fixed deposit = [(15L − 3x) × (6/100) × 1]&nbsp;...(1)Simple interest earned on 2x principle = 2x × (4/100) × 1 ...(2)Simple interest earned on x principle = x × (3/100) × 1 ...(3)(1) + (2) + (3) = 76000.Solving we get; x = 2L.So, amount invested in fixed deposit = 15L − 3x = 15L − 6L = 9L.Hence, 9.

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Simple And Compound Interest

Question 1.

<div>Amala, Bina, and Gouri invest money in the ratio 3 : 4 : 5 in fixed deposits having respective annual interest rates in the ratio 6 : 5 : 4. What is their total interest income (in Rs) after a year, if Bina's interest income exceeds Amala's by Rs 250?</div>

Question 2.

<div>A sum of money compounded annually becomes Rs. 625 in two years and Rs. 675 in three years. The rate of interest per annum is</div>

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Question 3.

<div>The total interest, in rupees, collected by Ghosh Babu was:</div>

Question 4.

<div>A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is</div>

Question 5.

<div>The year, at the end of which, Ghosh Babu withdrew the maximum amount was:</div>

Question 6.

<div>For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by Rs 1125. Then the principal amount in rupees is</div>

Question 7.

<div>The year, at the end of which, Ghosh Babu collected the maximum interest was:</div>

Question 8.

<div>Veeru invested Rs. 10,000 at 5% simple annual interest, and exactly after two years, Joy invested Rs. 8,000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?</div>