Study the following data carefully and answer the questions:The line g...
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
Rate of interest in scheme A = 15%
Amount invested by R in scheme A = Rs.4000
So, CI received by R from scheme A after 2 years:
4000 * (1 + 15/100)2 – 4000 = Rs.1290
Rate of interest in scheme B = 12%
Amount invested in scheme B = Rs.5000
So, SI received by R from scheme B after 3 years:
(5000 * 12 * 3)/100 = Rs.1800
Required ratio = 1290: 1800 = 43: 60