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Certain amount was deposited in two different accounts one giving Simp
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06 Apr 2023, 03:58
06 Apr 2023, 03:58
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52% (02:02) correct
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Certain amount was deposited in two different accounts one giving Simple Interest and the other giving Compound Interest.
The rate of interest was different for both the accounts.The amount under Simple Interest triples in 4 years whereas amount under compound interest doubles in 4 years.
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
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\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE SINGLE & COMPOUND INTEREST
The rate of interest was different for both the accounts.The amount under Simple Interest triples in 4 years whereas amount under compound interest doubles in 4 years.
Quantity A |
Quantity B |
Number of years inwhich the amount under Simple Interest will become 6 times of itself |
Number of years inwhich the amount under Cpmpound Interest will become 4 times of itself |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal
D. The relationship cannot be determined from the information given.
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE SINGLE & COMPOUND INTEREST
Re: Certain amount was deposited in two different accounts one giving Simp
[#permalink]
03 May 2023, 09:21
03 May 2023, 09:21
Expert Reply
OE
Let us assume the amount deposited in two different accounts be ๐ and ๐ต
respectively.
Given the amount under simple interest triples in 4 years and the amount under
compound interest doubles in 4 years.
Since the amount under simple interest triples in 4 years we get,
๐ 3 ๐
That means in 4 years, P gets increased by 3 ๐ - ๐ = 2 ๐.
This implies, in every 4 year, there is an increase of 2 ๐ in the amount.
โin every 2 year, there is an increase of ๐ in the amount.
GRE simple interest.jpg [ 25.6 KiB | Viewed 5077 times ]
So, we can see that after 4 years the amount is 3 ๐ and after 8 years it will be 5P.
To get the amount 6 times of itself, it would take 2 more years .
Hence, quantity A is 10 years .
Let us assume the amount deposited in two different accounts be ๐ and ๐ต
respectively.
Given the amount under simple interest triples in 4 years and the amount under
compound interest doubles in 4 years.
Since the amount under simple interest triples in 4 years we get,
๐ 3 ๐
That means in 4 years, P gets increased by 3 ๐ - ๐ = 2 ๐.
This implies, in every 4 year, there is an increase of 2 ๐ in the amount.
โin every 2 year, there is an increase of ๐ in the amount.
Attachment:
GRE simple interest.jpg [ 25.6 KiB | Viewed 5077 times ]
So, we can see that after 4 years the amount is 3 ๐ and after 8 years it will be 5P.
To get the amount 6 times of itself, it would take 2 more years .
Hence, quantity A is 10 years .
Re: Certain amount was deposited in two different accounts one giving Simp
[#permalink]
21 Jun 2024, 09:17
21 Jun 2024, 09:17
2
for the amount in compound interest, we know it doubles in 4 years, we can write the equation as:
p(1+r/100)^4= 2p
cancelling p from both sides
(1+r/100)^4=2
1+r/100=2^1/4--------equation(i)
we need to know the time in which amount becomes 4 times, we can write the equation as:
p(1+r/100)^t=4p
cancelling p
(1+r/100)^t=4
(2^1/4)^t= 2^2
t/4=2
which makes time as 8 years. meaning a (10 years as shown before)>b
p(1+r/100)^4= 2p
cancelling p from both sides
(1+r/100)^4=2
1+r/100=2^1/4--------equation(i)
we need to know the time in which amount becomes 4 times, we can write the equation as:
p(1+r/100)^t=4p
cancelling p
(1+r/100)^t=4
(2^1/4)^t= 2^2
t/4=2
which makes time as 8 years. meaning a (10 years as shown before)>b
