In the first year of a couple's marriage, the wife’s earnings were 40

Question

In the first year of a couple's marriage, the wife’s earnings were 40 percent of the combined earnings of the couple. The wife invested 40 percent of her earnings at an annual return of 5 percent and the husband invested 30 percent of his earnings at an annual return of 10 percent. In the second year of their marriage, the combined earnings of the couple increased by 10 percent and the wife’s earnings were five-sixths of her husband’s earnings. The wife invested 48 percent of her earnings and the husband invested 50 percent of his earnings in their respective investment instruments of the previous year. If the couple made no other investments and took out the interest earned in the first year at the beginning of the second year, by approximately what percent was the interest earned by the couple in the second year greater than the interest earned by the couple in the first year of their marriage? The interest income from the couple’s investments is not considered in their earnings.

A. 30%

B. 40%

C. 50%

D. 60%

E. 70%

A. 30%

B. 40%

C. 50%

D. 60%

E. 70%

nick1816 · Answer

Salary of Husband in the first year = 60 
Interest he gets = 60*0.3*10*x= 180x, where  x=\frac{1}{100 }

Salary of Wife in the first year = 40 
Interest she gets = 40*0.4*5*x= 80x

Total interest earned by the couple in the  first  year =  260x

Salary of Husband in the second year = 60 
Interest he gets = 60*0.5*10*x= 300x

Salary of Wife in the second year = 50 
Interest she gets = 40*0.48*5*x= 120x

Total interest earned by the couple in the  second  year =  420x

Increase in the interest =  \frac{420-260}{260} *100   = \frac{800}{13} ≈ \frac{780}{13} = 60  %

Skaa · Answer

Salary of Husband in the first year = 60 
Interest he gets = 60*0.3*10*x= 180x, where  x=\frac{1}{100 }

Salary of Wife in the first year = 40 
Interest she gets = 40*0.4*5*x= 80x

Total interest earned by the couple in the  first  year =  260x

Salary of Husband in the second year = 60 
Interest he gets = 60*0.5*10*x= 300x

Salary of Wife in the second year = 50 
Interest she gets = 40*0.48*5*x= 120x

Total interest earned by the couple in the  second  year =  420x

Increase in the interest =  \frac{420-260}{260} *100   = \frac{800}{13} ≈ \frac{780}{13} = 60  %

Can you please explain why x= 1/100

nick1816 · Answer

If the Salary of Husband in the first year = 60, amount, P, that he invested is 60*0.3 = 18

Annual Interest =  \frac{P*r*t}{100}  =  \frac{18*10*1}{100.}

Since we are finding percentage of increase in the interest, common terms (i.e is 1/100) gonna cancelled out in the last. So, i just substitute it with a random variable. Also, I personally don't like to involve fractions or decimals in my calculations (helps me to do most of the calculations mentally).

ScottTargetTestPrep · Answer

Solution:

Let the combined income of the couple in the first year be 1000. Then, the wife earned 0.4 * 1000 = 400 and the husband earned 1000 - 400 = 600. The wife invested 400 * 0.4 = 160 at 5% for a year; thus, the interest she earned was 160 * 0.05 = 8. The husband invested 600 * 0.3 = 180 at 10% for a year; thus, the interest he earned was 180 * 0.1 = 18. In total, the couple earned an interest of 8 + 18 = 26 in the first year.

In the second year, the couple earned 1000 * 1.1 = 1100 in total. Let h be the earnings of the husband. Then, the wife earned 5h/6 and in total, they earned h + 5h/6 = 11h/6. Setting this equal to 1100, we obtain:

11h/6 = 1100

h/6 = 100

h = 600

So, the husband earned 600 in the second year and the wife earned 1100 - 600 = 500. The wife invested 500 * 0.48 = 240 at 5% for a year; thus, she earned an interest of 240 * 0.05 = 12 in the second year. The husband invested 600 * 0.5 = 300 at 10% for a year; thus, he earned an interest of 300 * 0.1 = 30 in the second year. In total, the couple earned an interest of 30 + 12 = 42 in the second year.

We can use the percent greater than formula to obtain that the interest earned in the second year was 100 * (42 - 26)/26 = 100 * 16/26 ≈ 61.53 percent, which is approximately 60%.

Answer: D

ShaikhMoice · Answer

Thanks for the solution, just 1 query why are you not considering the interest earned in 2nd year from the investment made in the 1st year.
Thanks in Advance.

bumpbot · Answer

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In the first year of a couple's marriage, the wife’s earnings were 40

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