Jack invested an amount P at 6% annual rate of simple interest. Natila

Question

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Jack invested an amount  P  at 6% annual rate of simple interest. Natila invested an amount  2P  at 4% annual rate of simple interest. Jack stayed invested for a time period of  5T  years while Natila stayed invested for a time period of  3T  years. The total interest earned by Jack on his investment was $x and the total interest earned by Natila on her investment was $y.

In the table, select a value for x and a corresponding value for y. Make only two selections, one in each column.

chetan2u · Accepted Answer

Jack invested an amount  P  at 6% annual rate of simple interest. Natila invested an amount  2P  at 4% annual rate of simple interest. Jack stayed invested for a time period of  5T  years while Natila stayed invested for a time period of  3T  years. The total interest earned by Jack on his investment was $x and the total interest earned by Natila on her investment was $y.

Natila:  Principal = 2P; Rate = 4%; Time =3T…….Interest = y =  \frac{2P*4*3T}{100} 
 Jack:  Principal = P; Rate = 6%; Time =5T…….Interest = x =  \frac{P*6*5T}{100}

Thus  \frac{y}{x}=\frac{2P*4*3T}{P*6*5T}=\frac{4}{5}  or x=1.25y

Thus x>y. 
Find values that fit in as per this ratio. y=2000, x=1.25*2000=2500

AbhinavShah14 · Answer

Can Anyone solve this question?

Sajjad1994 · Answer

Official Explanation

The comparison of the two interest rates will be as follows:

Jack: x = P * 6 percent * 5T = 30 * TP

Natila: y = 2P * 4 percent * 3T = 24 * TP

So x:y are in ratio 5:4.

The only two options that are in this ratio are $2500 and $2000.

Gemmie · Answer

Jack: P - Simple interest - 6% annual - 5T years
=> total interest =  P * \frac{6}{100} * 5T = P * T * \frac{30}{100}

Natila: 2P - Simple interest - 4% annual - 3T years
=> total interet =  2P * \frac{4}{100} * 3T = P * T * \frac{24}{100}

\frac{Interest J }{ Interest N} = \frac{30}{24} = \frac{5}{4}

Interest J = x = 2500
Interest N = y = 2000

smruthilokesh · Answer

But why are we taking the ratio of x to y?

chetan2u · Answer

That is because you want a relationship between x and y so that you can choose a value each from the options.

x	y	Value
		$2,000
		$2,500
		$3,000
		$3,500
		$4,000

Jack invested an amount P at 6% annual rate of simple interest. Natila

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