A, B, and C invest money in the ratio 3:4:5 in fixed deposits having r

Solution:

Let 3x, 4x, and 5x be the investment made by A, B, and C respectively.
Let 6y, 5y, and 4y be the interest percentage for A, B, and C respectively.

• Interest amount of A = \( \frac{3x*6y*1}{100} = \frac{18xy}{100}\)
• Interest amount of B = \(\frac{4x*5y}{100}=\frac{20xy}{100}\)
• Interest amount of C = \(\frac{5x*4x}{100}\)=\(\frac{20xy}{100}\)

o Total interest earned = \(\frac{18xy}{100}+\frac{20xy}{100}+\frac{20xy}{100} = \frac{58xy}{100}\)
• Interest amount of B is $ 250 more than A

o \(\frac{20xy}{100}– \frac{18xy}{100} = 250\)
o \(\frac{2}{100}xy = 250\)
• Total interest earned = \(\frac{58xy}{100} = 29*\frac{2xy}{100}=29*250 = $ 7250\)

Hence, the correct answer is Option A

Simple Interest earned, SI is directly proportional to product of principal amount and rate of interest
--> Ratio of interests = 3*6 : 4*5 : 5*4 = 18 : 20 : 20
--> Values of interests of (A, B, C) = (18k, 20k, 20k) for some positive value 'k'

Given, 20k - 18k = 250
--> k = 125

--> Total interest = 18k + 20k + 20k = 58k = 58*125 = $7250

Option A

Alternatively

The ratio of investments is 3:4:5 for A, B, and C respectively.
The ratio of interest rates is 6:5:4 for A, B, and C respectively.
We know that B's interest income exceeds that of A by $250.

A's invested Amount = 3/12 * Tot Inv
B's invested Amount = 4/12 * Tot Inv

A's annual interest = 6/15 * 3/12 * Tot Inv = 18/180 * Tot Inv -----(1)
B's annual interest = 5/15 * 4/12 * Tot Inv = 20/180 * Tot Inv -----(2)
C's annual interest = 4/15 * 5/12 * Tot Inv = 20/180 * Tot Inv -----(3)

But we know that B's annual interest - A's annual interest = 250
Hence 250 = (20/180 - 18/180) * Tot Inv
250 = 2/180 * Tot Inv
Tot Inv = 250*90 = 22,500

B's Int = 18/180 * 22500 = 2,500
A's Int = 20/180 * 22500 = 2,250
C's Int = 20/180 * 22500 = 2,500

Total Int = 2500+2500+2250 = $7,250

A is the answer.

Answer A = 7250
See the attachment.