Study the following data carefully and answer the questions:The line graph given below shows four persons P, Q, R and S invested different amounts in two different schemes i.e., A and B and both the schemes give simple interest at different rate of interest.Note:1: Ratio of rate of interest in scheme A to that in scheme B is 5 : 4.2: Amount invested by R in scheme A is 2000 less than that invested by P in scheme A.If a person T invested Rs.2000 less than Q in scheme A and Rs.1500 less than Q in scheme B, then total simple interest received by T after 2 years from both the schemes together will be how much less than the interest received by Q after 2 years from both the schemes together?a)Rs.1440b)Rs.960c)Rs.1240d)Rs.880e)Rs.1080Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Let rates of interest in scheme A and scheme B are ‘5r’% and ‘4r’% respectively.

Also let the amount invested by P in scheme A = ‘a’ rupees

So, the amount invested by R in scheme A = (a – 2000) rupees

The amount invested by P in scheme B = (a + 1500) rupees

And the amount invested by R in scheme B = (a – 2000 + 1000) = (a – 1000) rupees

Now,

[(a * 5r * 2)/100] – [{(a + 1500) * 4r * 3}/100] = -900

10ar – (12ar + 18000r) = -90000

12ar + 18000r – 10ar = 90000

2ar + 18000r = 90000

ar + 9000r = 45000 ------------(1)

And,

[{(a – 2000) * 5r * 2}/100] – [{(a – 1000) * 4r * 3}/100] = -600

(10ar – 20000r) – (12ar – 12000r) = -60000

12ar – 12000r – 10ar + 20000r = 60000

2ar + 8000r = 60000

ar + 4000r = 30000 ------------(2)

From equations (1) and (2):

45000 – 9000r = 30000 – 4000r

r = 3

Rate of interest in scheme A = 5 * 3 = 15%

Rate of interest in scheme B = 4 * 3 = 12%

From equation (1):

3a + 27000 = 45000

a = 6000

Person P:

Amount invested in scheme A = Rs.6000

Amount invested in scheme B = (6000 + 1500) = Rs.7500

Person Q:

Let amount invested in scheme A = Rs.‘x’

And amount invested in scheme B = Rs.(x – 2500)

So,

[(x * 15 * 2)/100] – [{(x – 2500) * 12 * 3}/100] = 300

30x – (36x – 90000) = 30000

x = 10000

Amount invested in scheme A = Rs.10000

Amount invested in scheme B = (10000 – 2500) = Rs.7500

Person R:

Amount invested in scheme A = (6000 – 2000) = Rs.4000

Amount invested in scheme B = (6000 – 1000) = Rs.5000

Person S:

Let amount invested in scheme A = Rs.‘y’

And amount invested in scheme B = Rs.(y – 3000)

So,

[(y * 15 * 2)/100] – [{(y – 3000) * 12 * 3}/100] = 600

30y – (36y – 108000) = 60000

y = 8000

Amount invested in scheme A = Rs.8000

Amount invested in scheme B = (8000 – 3000) = Rs.5000

Answer: B

Amount invested by Q in scheme A = Rs.10000

So, amount invested by T in scheme A = 10000 – 2000 = Rs.8000

Amount invested by Q in scheme B = Rs.7500

So, amount invested by T in scheme B = 7500 – 1500 = Rs.6000

Now,

Total SI received by Q after 2 years from both the schemes together:

[(10000 * 15 * 2)/100] + [(7500 * 12 * 2)/100] = Rs.4800

And,

Total SI received by T after 2 years from both the schemes together:

[(8000 * 15 * 2)/100] + [(6000 * 12 * 2)/100] = Rs.3840

Required difference = 4800 – 3840 = Rs.960

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