"> Word Problem 12 | Job Exam Rare Mathematics (JEMrare)

Word Problem 12

Problem 12: A sum of Rs 1550 was lent partly at 5% and partly at 8% simple interest. The total interest received after 3 years was Rs 300. The ratio of amounts lent at 5% and 8% is;

a. 5:8                   b. 8:5                       c.31:6                    d. 16:15

Solution:

simple arithmetic questions and answers

R1=5%

R2=8%

Total Simple Interest = Rs 300

Time = 3 years

Money lent at 5% : Money lent at 8% =?

We start by supposing that;

Money Lent At 5%=yRs

So,

\Rightarrow Money Lent At 8%=(1550-y)Rs

So, for first amount;

Yearly Interest @ 5%= \frac{5y}{100}

For second amount part;

Yearly Interest @ 8%= \frac{8(1550-y)}{100}

So,

Total Interset Yearly= \frac{5y}{100}+\frac{8(1550-y)}{100}

But Yearly interest is calculated by dividing total interest by number of years!

From given data we can calculate it as;

Total Interset Yearly= \frac{Total Interest}{Number Of Years}

Total Interset Yearly= \frac{300}{3}=100

This interest  of given data and our calculated total interests should be same;

\Rightarrow \frac{5y}{100}+\frac{8(1550-y)}{100}=100

Solving for ‘y’

\Rightarrow 5y+8\times 1550-8y=10000

\Rightarrow y=800

So, money lent at 5% interest is Rs 800 and money lentat 8% interest is 1550-y = 1550-800= Rs 750

Their ratio is;

800:750

which finally settles to be

16:15

 

 

 

 

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