We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.More informationAgree
×
Custom Search
cancel
×
×
ad

# Solved Examples(Set 6) - Simple Interest

 26. David invested certain amount in three different schemes A, B and C with the rate of interest per annum $10\%, 12\%$ and $15\%$ respectively. If the total interest accrued in one year was $₹3200$ and the amount invested in Scheme C was $150\%$ of the amount invested in Scheme A and $240\%$ of the amount invested in Scheme B, what was the amount invested in Scheme B? A. $₹5000$ B. $₹3000$ C. $₹6000$ D. $₹2000$
 View Answer Discuss
answer with explanation

Answer: Option A

Explanation:

## Solution 1

Let investments in A,B,C be $x,y,z$

simple interest on $x$ at $10\%$ for $1$ year
+ simple interest on $y$ at $12\%$ for $1$ year
+ simple interest on $z$ at $15\%$ for $1$ year
$=3200$

$\dfrac{x×10×1}{100}+\dfrac{y×12×1}{100}+\dfrac{z×15×1}{100}=3200\\\Rightarrow 10x+12y+15z=320000 \quad \cdots(1)$

investment in Scheme C = $240\%$ of investment in scheme B
$\Rightarrow z=\dfrac{240y}{100}=\dfrac{12y}{5}\cdots\cdots(2)$

investment in Scheme C = $150\%$ of investment in scheme A
$\Rightarrow z=\dfrac{150x}{100}=\dfrac{3x}{2}\\\Rightarrow x=\dfrac{2z}{3}=\dfrac{2}{3}×\dfrac{12y}{5}=\dfrac{8y}{5} \cdots(3)$

Using $(2)$ and $(3)$ in $(1)$

$10x+12y+15z=320000\\\Rightarrow 10\left(\dfrac{8y}{5}\right)+12y+15\left(\dfrac{12y}{5}\right)=320000\\\Rightarrow 16y+12y+36y=320000\\\Rightarrow 64y=320000\\\Rightarrow y=5000$

That is, amount invested in Scheme B $=₹5000$

## Solution 2

scheme C investment $=150\%$ of scheme A investment
scheme C investment $=240\%$ of scheme B investment

Therefore, ratio of investments of A,B,C
$=100:150×\dfrac{100}{240}:150\\=8:5:12$
hint

Suppose scheme A investment $100$

Scheme C investment $=150\%$ of scheme A investment
$\Rightarrow$ scheme C investment $=150\%$ of $100$ $=150$

scheme C investment $=240\%$ of scheme B investment
$\Rightarrow$ scheme B investment $=\dfrac{100}{240}$ × scheme C investment
$\Rightarrow$ scheme B investment $=\dfrac{100}{240}×150$

Therefore, ratio of investments of A,B,C
$=100:150×\dfrac{100}{240}:150\\=8:5:12$

Ratio of rate of interest of A,B,C
$=10:12:15$

simple interest $\propto$ PR (because T is constant here)
Therefore, ratio of simple interests in A,B,C
$=8×10:5×12:12×15=4:3:9$

Interest on B $=3200×\dfrac{3}{4+3+9}=600$

Investment on B $=\dfrac{100×600}{12×1}=5000$

 27. A sum of $₹1550$ was lent partly at $5\%$ and partly at $8\%$ per annum simple interest. The total interest received after $3$ years was $₹300.$ The ratio of the money lent at $5\%$ to that lent at $8\%$ is: A. $15:16$ B. $16:15$ C. $15:8$ D. $8:15$
 View Answer Discuss
answer with explanation

Answer: Option B

Explanation:

## Solution 1

Let the partial amount lent at $5\%$ and $8\%$ be $x$ and $(1550-x)$ respectively.

simple interest on $x$ at $5\%$ for $3$ years + simple interest on $(1550-x)$ at $8\%$ for $3$ years $=300$

$\dfrac{x×5×3}{100}+\dfrac{(1550-x)×8×3}{100}=300\\\Rightarrow 5x+8(1550-x)=10000\\\Rightarrow 5x+12400-8x=10000\\\Rightarrow 3x=2400\\\Rightarrow x=800$

Required ratio $=x:(1550-x)=800:(1550-800)=800:750=16:15$

## Solution 2

simple interest on $1550$ at $5\%$ for $3$ years $=\dfrac{1550×5×3}{100}=232.5$

Therefore, part amount invested at $8\%$ has earned the additional interest of $(300-232.5)$ at the interest rate of $(8-5)\%$ in $3$ years.

Therefore, part amount invested at $8\%$ $=\dfrac{100×67.5}{3×3}=750$

Part amount invested at $5\%$ $=1550-750=800$

Required ratio $=800:750=16:15$

 28. A sum of money doubles in $12$ years. In how many years, will it treble (assume simple interest)? A. $24$ B. $8$ C. $12$ D. $6$
 View Answer Discuss
answer with explanation

Answer: Option A

Explanation:

## Solution 1

Let the sum be $x.$ Assume that it will treble in $n$ years.

Note that when the money doubles, simple interest is $(2x-x)$ and when the money trebles, simple interest is $(3x-x)$

simple interest $\propto$ T (because here P and R are constants)

Therefore,
$(2x-x):(3x-x)=12:n\\\Rightarrow x:2x=12:n\\\Rightarrow n=24$

## Solution 2

Given that the sum doubles in $12$ years. This means, simple interest is equal to the sum in $12$ years.

Therefore, simple interest will be double the sum in $24$ years. That is, it will treble in $24$ years.

 29. A man invests a certain sum of money at $6\%$ per annum simple interest and another sum at $7\%$ per annum simple interest. His income from interest after $2$ years was $₹354.$ One-forth of the first sum is equal to one-fifth of the second sum. What was the total sum invested? A. $₹2200$ B. $₹3100$ C. $₹2700$ D. $₹1800$
 View Answer Discuss
answer with explanation

Answer: Option C

Explanation:

## Solution 1

Let the first sum and second sum be $4x$ and $5x$ respectively (hint).

To make calculations easier, we have taken the first and second sum as $4x$ and $5x$ which satisfies the condition that one-forth of first sum equals one-fifth of second sum.

Simple interest on first sum at $6\%$ for $2$ years + simple interest on second sum at $7\%$ for $2$ years $=354$
$\Rightarrow \dfrac{4x×6×2}{100}+\dfrac{5x×7×2}{100}=354\\\Rightarrow 4x×6+5x×7=17700\\\Rightarrow 59x=17700\\\Rightarrow x=300$

Total sum invested $=4x+5x=9x=2700$

## Solution 2

Let the sum invested at $6\%$ and $7\%$ be $x$ and $y$ respectively.

Simple interest on $x$ at $6\%$ for $2$ years + simple interest on $y$ at $7\%$ for $2$ years $=354$
$\Rightarrow \dfrac{x×6×2}{100}+\dfrac{y×7×2}{100}=354\\\Rightarrow 6x+7y=17700 ~\cdots(1)$

One-forth of the first sum is equal to one-fifth of the second sum
$\Rightarrow \dfrac{x}{4}=\dfrac{y}{5}\\\Rightarrow x=\dfrac{4y}{5}\quad \cdots (2)$

Solving $(1)$ and $(2),$
$6x+7y=17700\\\Rightarrow 6\left(\dfrac{4y}{5}\right)+7y=17700\\\Rightarrow 24y+35y=17700×5\\\Rightarrow 59y=17700×5\\\Rightarrow y=1500$

$x=\dfrac{4y}{5}=\dfrac{4×1500}{5}=1200$

Total sum invested $=x+y=1500+1200=2700$

 30. Simple interest on a certain deposit at $5\%$ per annum in one year is $₹101.20.$ How much will be the additional simple interest on the same deposit at $6\%$ per annum in one year? A. $₹20.24$ B. $₹19.74$ C. $₹20.8$ D. $₹19.5$
 View Answer Discuss
answer with explanation

Answer: Option A

Explanation:

## Solution 1

$\text{P}=\dfrac{100×101.20}{5×1}=2024$

Simple interest on $₹2024$ at $6\%$ per annum for $1$ year $=\dfrac{2024×6×1}{100}=121.44$

Additional simple interest $=121.44-101.20=20.24$

## Solution 2

$\text{P}=\dfrac{100×101.20}{5×1}=2024$

Additional interest rate $=6\%-5\%=1\%$

Additional simple interest = simple Interest on $₹2024$ at $1\%$ per annum for $1$ year
$=\dfrac{2024×1×1}{100}=20.24$

## Solution 3

Additional interest rate $=6\%-5\%=1\%$

$5\%\implies 101.20\\1\% \implies \dfrac{101.20×1}{5}=20.24$

Therefore, additional simple interest is $20.24$

## Add Your Comment

(use Q&A for new questions)
Name
preview