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# A bank lent \$4000 to Jack at a certain rate of simple interest and \$50

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Senior Manager
Joined: 25 Dec 2018
Posts: 487
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
A bank lent \$4000 to Jack at a certain rate of simple interest and \$50  [#permalink]

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05 Mar 2019, 23:05
1
00:00

Difficulty:

55% (hard)

Question Stats:

50% (02:18) correct 50% (03:27) wrong based on 22 sessions

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A bank lent \$4000 to Jack at a certain rate of simple interest and \$5000 to Kate at a rate which is 0.5% more than that of Jack. After two years, the bank received \$860 as interest from both of them. Find the rate of interest per annum at which the amount was lent to Kate?

A. 4.5%
B. 4%
C. 5.5%
D. 5%
E. 8%
Manager
Joined: 12 Apr 2011
Posts: 149
Location: United Arab Emirates
Concentration: Strategy, Marketing
Schools: CBS '21, Yale '21, INSEAD
GMAT 1: 670 Q50 V31
GMAT 2: 720 Q50 V37
WE: Marketing (Telecommunications)
Re: A bank lent \$4000 to Jack at a certain rate of simple interest and \$50  [#permalink]

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06 Mar 2019, 11:41
1
mangamma wrote:
A bank lent \$4000 to Jack at a certain rate of simple interest and \$5000 to Kate at a rate which is 0.5% more than that of Jack. After two years, the bank received \$860 as interest from both of them. Find the rate of interest per annum at which the amount was lent to Kate?

A. 4.5%
B. 4%
C. 5.5%
D. 5%
E. 8%

Let us consider the rate of interest for Jack = x% per annum
Hence for Kate = (x+0.5)%

Simple interest for Jack for 2 years = 2 * 4000 * (x/100) = 80x
Simple interest for Kate for 2 years = 2 * 5000 * (x+0.5/100) = 100x + 50
Now we also know that:

80x + 100x + 50 = 860
=> 180x = 810
=> x = 4.5%

Hence RoI for Jack = 4.5%
RoI for Kate = 5%

Hence D is the correct answer.
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Re: A bank lent \$4000 to Jack at a certain rate of simple interest and \$50   [#permalink] 06 Mar 2019, 11:41
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