Question
At the rate of simple interest per annum, the interest on a certain sum of money for 10 years will be $2/5$th part of the amount, then the rate of simple interest is
Answer: Option A
Answer: (a)Amount after 10 years= P$(1 + {RT}/100)$ = P$(1 + {R × 10}/100)$= Rs. P$(1 + R/10)$Interest = Rs.P$(1 + R/10) × 2/5$Rate= ${\text"SI" × 100}/\text"Principal × Time"$R = ${P(1 + R/10) × 2/5 × 100}/{P × 10}$R = 4$(1 + R/10)$$R/4 = 1 + R/10$$R/4 - R/10$ = 1${5R - 2R}/20$ = 13R = 20R = $20/3 = 6{3}2%$Using Rule 5,Here, S.I. = $2/5$ amountS.I. = $2/5$ (P + S.I.)S.I. = $2/5$ S.I. + $2/5$ P$3/5$ S.I. = $2/5$ PS.I. = $2/3$PNow, n = $2/3$, T = 10 years.R= ${n × 100}/T$= $2/3 × 100/10$= $20/3 = 6{2}/3%$
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Answer: (a)Amount after 10 years= P$(1 + {RT}/100)$ = P$(1 + {R × 10}/100)$= Rs. P$(1 + R/10)$Interest = Rs.P$(1 + R/10) × 2/5$Rate= ${\text"SI" × 100}/\text"Principal × Time"$R = ${P(1 + R/10) × 2/5 × 100}/{P × 10}$R = 4$(1 + R/10)$$R/4 = 1 + R/10$$R/4 - R/10$ = 1${5R - 2R}/20$ = 13R = 20R = $20/3 = 6{3}2%$Using Rule 5,Here, S.I. = $2/5$ amountS.I. = $2/5$ (P + S.I.)S.I. = $2/5$ S.I. + $2/5$ P$3/5$ S.I. = $2/5$ PS.I. = $2/3$PNow, n = $2/3$, T = 10 years.R= ${n × 100}/T$= $2/3 × 100/10$= $20/3 = 6{2}/3%$
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