A certain sum of money lent out at simple interest amounts to Rs 800 in 2 years and Rs 1600 in 6 years. Find the rate percent per annum ?
Answers
Answer:
50%
Explanation:
Let principal be = P
and Rate of interest = R
According to question
= Amount = Rs 800
= Time = 2 years
And
=Amount = Rs 1600
=Time = 6 years
For 2 years
SI = P×R×T/100
= P×R×2/100 = 2PR/100
= Amount = P+SI
=800 = P+2PR/100
For 6 years
SI = P×R×T/100
= P×R×T/100
= P×R×6/100 = 6PR/100
=Amount = P+SI
=1600= P+6PR/100
NOW
SI in 2 years : subtract eq1 from eq2
= 1600 - 800 = P+ (6PR/100) - {P+(2PR/100)}
= 800 = P + (6PR/100) - P-(2PR/100)
= 800 = P-P + (6PR/100) - (2PR/100)
= 800 = (6 PR -2PR /100)
= 800 = 4PR/100
= PR/100 = 800/4
= PR/100= 200
EQ 1
= 800= P + (2PR/100)
= 800 = P + (2×200)
= 800 = P + 400
= P = 800 - 400
= P = Rs 400
= PR/100 = 200
= 400R/100= 200
= 4R = 200
R= 200/4
R= 50%
hope this helps :D
Given data : A certain sum of money lent out at simple interest amounts to Rs 800 in 2 years and Rs 1600 in 6 years.
To find : Find the rate percent per annum ?
Solution : Let, principal be P and rate of interest be R.
A/C to question;
➜ A (amount) = Rs 800
➜ T (time period) = 2 years and
➜ A = Rs 1600
➜ T = 6 years
Now, a/c to given data;
For 2 years,
➜ S.I (simple interest) = (P * R * T)/100
➜ S.I (simple interest) = (P * R * 2)/100
➜ S.I (simple interest) = 2PR/100
Here, we know
➜ Amount = principal + simple interest
➜ 800 = P + (2PR/100) ----{1}
Similarly,
For 6 years,
➜ S.I (simple interest) = (P * R * T)/100
➜ S.I (simple interest) = (P * R * 6)/100
➜ S.I (simple interest) = 6PR/100
Now,
➜ Amount = principal + simple interest
➜ 1600 = P + (6PR/100) ----{2}
Now,
Simple interest for 4 years : subtract eq. {1} from eq. {2}
➜ 1600 - 800 = P + (6PR/100) - {P + (2PR/100)}
➜ 800 = P + (6PR/100) - P - (2PR/100)
➜ 800 = P - P + (6PR/100) - (2PR/100)
➜ 800 = (6PR - 2PR)/100
➜ 800 = 4PR/100
➜ PR/100 = 800/4
➜ PR/100 = 200 ----{3}
Now, put value of PR/100 in eq. {1}
➜ 800 = P + (2PR/100)
➜ 800 = P + (2 * 200)
➜ 800 = P + 400
➜ P = 800 - 400
➜ P = Rs 400
To find out the rate of interest, percent per annum : Put value of P in eq. {3}
➜ PR/100 = 200
➜ 400R/100 = 200
➜ 4R = 200
➜ R = 200/4
➜ R = 50 %
Answer : Hence, the rate of interest, percent per annum is 50 %.