Question

ind Time when
(i) Principal = Rs. 6000, S.I. = Rs. 1052 and
Rate = 8% p.a.
ii) Principal = Rs. 4000, Amount = Rs. 5450
and Rate = 12% p.a.​

Answer 1

Step-by-step explanation:

Question 1:-

$\frak Given = \begin{cases} &\sf{Pricipal\ =\ Rs.\ 6000.} \\ &\sf{S.I\ =\ Rs.\ 1052.} \\ &\sf{Rate\ =\ 8\ \%\ p.a.} \end{cases}$

To find:- We have to find the time ?

__________________

$\frak{\underline{\underline{\dag As\ we\ know\ that:-}}}$

$\sf : \implies {S.I\ =\ \dfrac{(P\ \times\ R\ \times\ T)}{100}}$

Here:-

• S.I, for simple interest.
• P, is for principal.
• R, is for rate.
• T, is for time.

__________________

$\frak{\underline{\underline{\dag By\ substituting\ the\ values,\ we\ get:-}}}$

$\sf : \implies {1052\ =\ \dfrac{(6000\ \times\ 8\ \times\ T)}{100}} \\ \\ \sf : \implies {T\ =\ \dfrac{(1052\ \times\ 100)}{(6000\ \times\ 8)}} \\ \\ \sf : \implies {T\ =\ \dfrac{105200}{48000}} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf Time\ =\ 2.19\ years.}}}}\bigstar$

Hence:-

$\sf \therefore {\underline{The\ required\ time\ is\ 2.19\ years.}}$

__________________

Question 2:-

$\frak Given = \begin{cases} &\sf{Pricipal\ =\ Rs.\ 4000.} \\ &\sf{Amount\ =\ Rs.\ 5450.} \\ &\sf{Rate\ =\ 12\ \%\ p.a.} \end{cases}$

To find:- We have to find the time ?

__________________

$\frak{\underline{\underline{\dag As\ we\ know\ that:-}}}$

$\sf : \implies {S.I\ =\ Amount\ -\ Principal} \\ \\ \sf : \implies {S.I\ =\ 5450\ -\ 4000} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf S.I\ =\ Rs.\ 1450.}}}}\bigstar$

__________________

$\frak{\underline{\underline{\dag Now\ here:-}}}$

$\sf : \implies {S.I\ =\ \dfrac{(P\ \times\ R\ \times\ T)}{100}}$

Here:-

• S.I, is for simple interest.
• P, is for principal.
• R, is for rate.
• T, is for time.

__________________

$\frak{\underline{\underline{\dag By\ substituting\ the\ values,\ we\ get:-}}}$

$\sf : \implies {1450\ =\ \dfrac{(4000\ \times\ 12\ \times\ T)}{100}} \\ \\ \sf : \implies {T\ =\ \dfrac{(1450\ \times\ 100)}{(4000\ \times\ 12)}} \\ \\ \sf : \implies {T\ =\ \dfrac{145000}{48000}} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf Time\ =\ 3.02\ years.}}}}\bigstar$

Hence:-

$\sf \therefore {\underline{The\ required\ time\ is\ 3.02\ years.}}$

Answer 2

$\huge{\fcolorbox{yellow}{red}{\large{\fcolorbox{blue}{pink}{{\fcolorbox{orange}{aqua}{✨ANSWER✨}}}}}}$

▪︎1) Time = 2.19 year

▪︎2) Time = 3.02 year

Step-by-step explanation:

(1) Principal = Rs. 6000, S.I. = Rs. 1052 and Rate = 8% p.a.

We know that,

→ Simple Interest = ( Principal × Rate × Time ) / 100

→ 1052 = ( 6000 × 8 × Time ) / 100

→ Time = ( 1052 × 100 ) / ( 6000 × 8 )

→ Time = 105200 / 48000

→ Time = 2.19

☆ Time = 2.19 year . Ans i

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2) Principal = Rs. 4000, Amount = Rs. 5450 and Rate = 12% p.a.

We know that,

→ Simple Interest = Amount - Principal

→ Simple Interest = 5450 - 4000

→ Simple Interest = 1450

→ Simple Interest = ₹1450

We know that,

→ Simple Interest = ( Principal × Rate × Time ) / 100

→ 1450 = ( 4000 × 12 × Time ) / 100

→ Time = ( 1450 × 100 ) / ( 4000 × 12 )

→ Time = 145000 / 48000

→ Time = 3.02

☆ Time = 3.02 year . Ans ii