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Smith and Tom earn a combined profit of $4880 in their business and in 12 Nov 2019, 00:04
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61% (02:42) correct 39% (02:49) wrong based on 177 sessions

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Smith and Tom earn a combined profit of $4880 in their business and invest their share at 20% compounded annually at the same time. If the amount earned by Smith after 10 years is same as amount earned by Tom after 12 years. Find the amount invested by Smith.

A. $2880
B. $2640
C. $2520
D. $2440
E. $2000
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A
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Smith and Tom earn a combined profit of $4880 in their business and in 12 Nov 2019, 00:15
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Dillesh4096
Smith and Tom earn a combined profit of $4880 in their business and invest their share at 20% compounded annually at the same time. If the amount earned by Smith after 10 years is same as amount earned by Tom after 12 years. Find the amount invested by Smith.

A. $2880
B. $2640
C. $2520
D. $2440
E. $2000
Show more


Let the amount by smith be S, so by Tom it is 4880-S..
Smith : Amount after 10 years = \(S(1+\frac{20}{100})^{10}\)
Tom : Amount after 12 years = \((4880-S)(1+\frac{20}{100})^{12}\)

As both amounts are same....
\(S(1+\frac{20}{100})^{10}=(4880-S)(1+\frac{20}{100})^{12}.........S=(4880-S)(1+\frac{20}{100})^{2}=(4880-S)*(\frac{6}{5})^2...........S+\frac{36S}{25}=4880*\frac{36}{25}.......\)..
\(\frac{61S}{25}=4880*\frac{36}{25}...........S=4880*\frac{36}{25}*\frac{25}{61}=80*36=2880\)

A
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Smith and Tom earn a combined profit of $4880 in their business and in 19 Jul 2023, 08:19
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Dillesh4096
Smith and Tom earn a combined profit of $4880 in their business and invest their share at 20% compounded annually at the same time. If the amount earned by Smith after 10 years is same as amount earned by Tom after 12 years. Find the amount invested by Smith.

A. $2880
B. $2640
C. $2520
D. $2440
E. $2000
Show more

Solution:

  • Tom's investment and Smit's investment equated in 12 and 10 years. So, the difference is 2 years.
  • First of all, this clearly means Smith's investment was more than Tom's. You can eliminate options D and E here

  • Because of the difference in 2 years, we can infer that \(\frac{Smith}{Tom}=(1.2)^2=1.44\)
  • So, we can write \(Smith+\frac{Smith}{1.44}=4880\) or \(Smith=2880\)

Hence the right answer is Option A
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Smith and Tom earn a combined profit of $4880 in their business and in 19 Jul 2023, 08:33
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SaquibHGMATWhiz
Dillesh4096
Smith and Tom earn a combined profit of $4880 in their business and invest their share at 20% compounded annually at the same time. If the amount earned by Smith after 10 years is same as amount earned by Tom after 12 years. Find the amount invested by Smith.

A. $2880
B. $2640
C. $2520
D. $2440
E. $2000

Solution:

  • Tom's investment and Smit's investment equated in 12 and 10 years. So, the difference is 2 years.
  • First of all, this clearly means Smith's investment was more than Tom's. You can eliminate options D and E here

  • Because of the difference in 2 years, we can infer that \(\frac{Smith}{Tom}=(1.2)^2=1.44\)
  • So, we can write \(Smith+\frac{Smith}{1.44}=4880\) or \(Smith=2880\)

Hence the right answer is Option A
Show more

Hi Saquib,

Can you please elaborate on this part "Because of the difference in 2 years, we can infer that \(\frac{Smith}{Tom}\)=(1.2)^2=1.44"?

Thanks in advance. :)
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Smith and Tom earn a combined profit of $4880 in their business and in 31 Jul 2023, 05:29
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Dillesh4096
Smith and Tom earn a combined profit of $4880 in their business and invest their share at 20% compounded annually at the same time. If the amount earned by Smith after 10 years is same as amount earned by Tom after 12 years. Find the amount invested by Smith.

A. $2880
B. $2640
C. $2520
D. $2440
E. $2000

Solution:

  • Tom's investment and Smit's investment equated in 12 and 10 years. So, the difference is 2 years.
  • First of all, this clearly means Smith's investment was more than Tom's. You can eliminate options D and E here

  • Because of the difference in 2 years, we can infer that \(\frac{Smith}{Tom}=(1.2)^2=1.44\)
  • So, we can write \(Smith+\frac{Smith}{1.44}=4880\) or \(Smith=2880\)

Hence the right answer is Option A

Hi Saquib,

Can you please elaborate on this part "Because of the difference in 2 years, we can infer that \(\frac{Smith}{Tom}\)=(1.2)^2=1.44"?

Thanks in advance. :)
Show more

would love for an explanation as well
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Smith and Tom earn a combined profit of $4880 in their business and in 31 Jul 2023, 05:30
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chetan2u
Dillesh4096
Smith and Tom earn a combined profit of $4880 in their business and invest their share at 20% compounded annually at the same time. If the amount earned by Smith after 10 years is same as amount earned by Tom after 12 years. Find the amount invested by Smith.

A. $2880
B. $2640
C. $2520
D. $2440
E. $2000


Let the amount by smith be S, so by Tom it is 4880-S..
Smith : Amount after 10 years = \(S(1+\frac{20}{100})^{10}\)
Tom : Amount after 12 years = \((4880-S)(1+\frac{20}{100})^{12}\)

As both amounts are same....
\(S(1+\frac{20}{100})^{10}=(4880-S)(1+\frac{20}{100})^{12}.........S=(4880-S)(1+\frac{20}{100})^{2}=(4880-S)*(\frac{6}{5})^2...........S+\frac{36S}{25}=4880*\frac{36}{25}.......\)..
\(\frac{61S}{25}=4880*\frac{36}{25}...........S=4880*\frac{36}{25}*\frac{25}{61}=80*36=2880\)

A
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The question states that the profits are the same, not the amount. so why is this right?
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Smith and Tom earn a combined profit of $4880 in their business and in 31 Jul 2023, 22:06
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ChandlerBong
SaquibHGMATWhiz
Dillesh4096
Smith and Tom earn a combined profit of $4880 in their business and invest their share at 20% compounded annually at the same time. If the amount earned by Smith after 10 years is same as amount earned by Tom after 12 years. Find the amount invested by Smith.

A. $2880
B. $2640
C. $2520
D. $2440
E. $2000

Solution:

  • Tom's investment and Smit's investment equated in 12 and 10 years. So, the difference is 2 years.
  • First of all, this clearly means Smith's investment was more than Tom's. You can eliminate options D and E here

  • Because of the difference in 2 years, we can infer that \(\frac{Smith}{Tom}=(1.2)^2=1.44\)
  • So, we can write \(Smith+\frac{Smith}{1.44}=4880\) or \(Smith=2880\)

Hence the right answer is Option A

Hi Saquib,

Can you please elaborate on this part "Because of the difference in 2 years, we can infer that \(\frac{Smith}{Tom}\)=(1.2)^2=1.44"?

Thanks in advance. :)
Show more

Sure. Here it is.

Smith's amount in 10 years = Tom's amount in 12 years

\(⇒Smith\times (1.2)^{10}=Tom\times (1.2)^{12}\)

\(⇒Smith=Tom\times (1.2)^2\)

\(⇒\frac{Smith}{Tom}=(1.2)^2=1.44\)
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