Question

Rohan deposited rp5,000 at 8% per annum for 3 1/2 years and Sunil deposited rp5,000 at 6% per annum for four years.who will get more interest what ammount will get​

Answer 1

➤ Given :-

Principle (Rohan) :- ₹5000

Rate of interest (Rohan) :- 8%

Time (Rohan) :- 3½ years

Principle (Sunil) :- ₹5000

Rate of interest (Sunil) :- 6%

Time (Sunil) :- 4 years

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➤ To Find :-

• Who will get more interest.
• Total amount of both.

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➤ Formula required :-

Simple Interest :-

${\tt \large \dashrightarrow \orange{\boxed{\tt \gray{\dfrac{P \times R \times T}{100}}}}}$

Total amount :-

${\tt \large \dashrightarrow \orange{\boxed{\tt \gray{Simple \: Interest + Principle}}}}$

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★ How to do :-

Here, we are given that two boys deposits the same amount of money in a bank at some rate interest and time. We have asked that who gets the more interest and also we should calculate the total amount of both the boys. So, first we should find the simple interest of both boys using the first formula and then we should compare their interests to find who got more. Later, we can find thr total amount of both using the second formula given.

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➤ Solution :-

Simple Interest of Rohan :-

${\tt \leadsto \dfrac{5000 \times 8 \times 7}{100 \times 2}}$

${\tt \leadsto \dfrac{\cancel{5000} \times 8 \times 7}{\cancel{100} \times 2} = \dfrac{50 \times 8 \times 7}{1 \times 2}}$

${\tt \leadsto \dfrac{\cancel{50} \times 8 \times 7}{1 \times \cancel{2}} = \dfrac{25 \times 8 \times 7}{1 \times 1}}$

${\tt \leadsto 25 \times 8 \times 7}$

${\tt \leadsto 200 \times 7 = \boxed{\tt 1400}}$

Simple Interest of Sunil :-

${\tt \leadsto \dfrac{5000 \times 6 \times 4}{100}}$

${\tt \leadsto \dfrac{\cancel{5000} \times 4 \times 6}{\cancel{100}} = \dfrac{50 \times 4 \times 6}{1}}$

${\tt \leadsto 50 \times 4 \times 6}$

${\tt \leadsto 200 \times 6 = \boxed{\tt 1200}}$

Comparision :-

${\tt \leadsto 1400 \: \: and \: \: 1200}$

${\tt \leadsto 1400 \: \boxed{ > } \: 1200}$

Now,

Total amount of Rohan :-

${\tt \leadsto 1400 + 5000}$

${\tt \leadsto \boxed{ \tt Rs \: \: 6400}}$

Total amount of Sunil :-

${\tt \leadsto 1200 + 5000}$

${\tt \leadsto \boxed{ \tt Rs \: \: 6200}}$

$\Huge\therefore$ Rohan's interest is greater than Sunil.

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$\dashrightarrow$ Some related formulas :-

${\sf \longrightarrow \boxed{\sf Principle = \dfrac{SI \times 100}{R \times T}}}$

${\sf \longrightarrow \boxed{\sf Rate \: of \: Interest = \dfrac{SI \times 100}{P \times T}}}$

${\sf \longrightarrow \boxed{\sf Time = \dfrac{SI \times 100}{P \times R}}}$