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

Question

A, B, and C 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 $) after a year, if B's interest income exceeds A's by $250?

A. 7250
B. 7000
C. 6350
D. 6250
E. 6000

Are You Up For the Challenge: 700 Level Questions

A. 7250
B. 7000
C. 6350
D. 6250
E. 6000

Are You Up For the Challenge: 700 Level Questions

GMATinsight · Accepted Answer

Interest income of A = 3*6 = 18x
Interest income of B = 4*5 = 20x
Interest income of C = 5*4 = 20x

20x - 18x = 2x = 250 
i.e. x = 125

total interest = 18x+20x+20x = 58x = 58*125 = 7250

Answer:Option A

EgmatQuantExpert · Answer

Solution

Given  
In this question, we are given that
 • A, B, and C invest money in the ratio 3:4:5 in fixed deposits having respective annual interest rates in the ratio 6:5:4. 
• B's interest income exceeds A's by $250.

To find  
We need to determine
 • Total interest income of all (in $), after a year.

Approach and Working out  
Let us assume that the investments of A, B and C are 300i, 400i, and 500i respectively.
Also, the interest rates are 6r%, 5r%, and 4r% respectively.
 • Hence, interest for A = 6r% of 300i = 18ri
• Interest for B = 5r% of 400i = 20ri
• Interest for C = 4r% of 500i = 20ri

As per the given condition, 20ri – 18ri = 250
 Or, ri = 125

Therefore, total interest = 18ri + 20ri + 20ri = 58ri = 58 x 125 = 7250

Thus, option A is the correct answer.

Correct Answer: Option A

GMATWhizTeam · Answer

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

CareerGeek · Answer

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

eakabuah · Answer

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.

sambitspm · Answer

Answer A = 7250
See the attachment.

bumpbot · Answer

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

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

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