Math, asked by priyanshu4061, 11 months ago

Divide ₹2500 into 2 parts such that the simple intrest on one at 4% per annum for 5 years is double that on the
other at 5% per annum for 3 years

Answers

Answered by Anonymous
56

AnswEr :

\:\: \: \: \: \: \: \: \: \: \: \:\: \: \: \sf{Rs. \:2500} \\ \: \: \: \: \: \: \: \large{\: \: \:  \: \: \swarrow \: \: \: \: \: \: \: \: \searrow} \\ \: \: \:\underline{\tt1st \:part} \: \: \: \: \: \: \: \:\underline{ \tt2nd \:part} \\ \: \: \:\sf{Rs.\:x}\: \: \: \: \: \: \: \: \: \: \: \: \:\sf{Rs.(2500 - x)}

\bold{1st \:Part} \begin{cases}\sf{Principal(P_1)=Rs. \:x}\\\sf{Rate(R_1)=4 \% \: p.a.}\\ \sf{Time(T_1)=5\: Years}\end{cases}

\bold{2nd \:Part} \begin{cases}\sf{Principal(P_2)=Rs.(2500 - x)}\\\sf{Rate(R_2)=5\% \: p.a.}\\ \sf{Time(T_2)=3\:Years}\end{cases}

\rule{300}{1}

According to the Question Now :

\longrightarrow \tt 1st \:Part = 2 \times 2nd \:Part \\ \\\longrightarrow \tt \dfrac{P_1 R_1 T_1}{100} = 2 \times\dfrac{P_2 R_2 T_2}{100} \\ \\\longrightarrow \tt \dfrac{x \times 4 \times 5}{\cancel{100}} = 2 \times\dfrac{(2500 - x) \times5  \times 3}{ \cancel{100}} \\ \\\longrightarrow \tt20x = 30 \times (2500 - x) \\ \\\longrightarrow \tt20x = 75000 - 30x \\ \\\longrightarrow \tt20x + 30x = 75000 \\ \\\longrightarrow \tt50x = 75000 \\ \\\longrightarrow \tt x =  \cancel\dfrac{75000}{50} \\ \\\longrightarrow \large\tt x  = Rs. 1500

\rule{300}{2}

◗ 1st Part = x = Rs. 1500

◗ 2nd Part = (2500 - x) = Rs. 1000

1st part will be Rs. 1500 and 2nd Part will be Rs. 1000 respectively.

#answerwithquality #BAL

Answered by Itsritu
44

 \: 1st\: part \:  =  \: 2 \times 2nd \: part \: .

 \frac{x \:  \times  \: 4 \:  \times  \: 5}{100}  = 2 \times  \frac{(2500 -  \: x) \:  \times  \: 5 \:  \times  \:  3}{100}

20x \:  = 30 \: ( \: 2500 \:  -  \: x).

20x \:  =  \: 75000 \:  -  \: 30x \: .

20x \:  +  \: 30x \:  =  \: 75000.

50x \:  =  \: 75000.

x = \ \frac{75000}{50} .

x =  \: 1500.

first \: part \:  =  \: x \:  =  \:rs \:  1500.

second \: part \:  =  ( \: 2500 \:  -  \: x)\:  =  \: rs \: = 1000.

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