Simple Interest

Given principal, p = 1092 ₹,
rate of interest r= 10%,
time, n = 7 years
Simple interest, SI = (p×n×r)/100
⇒ SI = (1092×7×10)/100
⇒ SI = 764.4
At the end of 7 years, interest earned is ₹ 764.4

Let the sum be P.
⇒ Then, ((P × 7 × 23)/12 × 100) - ((P × 7 × 19)/ 12 × 100 ) = 672
⇒ or, 161P - 133P = 672 × 100 × 12
⇒ P = ((672 × 100 × 12)/28) = ₹ 28800
Hence, option (B) is correct.

Given principal, p = 5872 ₹,
rate of interest r= 9%,
time, n = 8 years
Simple interest, SI = (p×n×r) /100
⇒ SI = (5872×8×9) /100
⇒SI = 4227.84
⇒ At the end of 8 years, interest earned is ₹ 4227.84

Principal, p = 8000 ₹,
Rate of interest, r = 12% and
Time, t = 3 $$\frac{1}{2}$$ = 7/2 years
Simple Interest, S.I = ( p×t×r) / 100
S.I = (8000×12×7) / (2×100) = 3360
Amount to be paid = Principal + S.I
= 8000 + 3360 = 11, 360
Amount paid = 9000 and a goat.
⇒ 9000 + Goat = 11,360
⇒ Goat = 2360
Price of goat = 2360 ₹

Let the sum be ₹ 100.
SI = PNR/100
SI for first 6 months = (100×1×10)/(100×2) = ₹ 5
New principal = 100 + 5 = ₹ 105
SI fo last 6 months = (105×1×10)/(100×2) = ₹ 5.25
∴ amount at the end of 1 yr = 100 + 5 + 5.25
= ₹ 110.25
Effective rate = 110.25 - 100 = 10.25%:

Explanation:
Let the principal be P and rate be R
Then,
ratio = (P∗R∗6/100)/ P∗R∗9/100)
=6PR/9PR
=2:3

(12($$\frac{1}{2}$$)% - 10%)×= 1250
(25/2% - 10%)×= 1250
5/200×= 1250
1/40×= 1250
x = 50,000

We know that,
3 years = 1500
5 yr = 2000
Then SI for 2 yearss (5yrs - 3 yearss) = 500
SI for 1 yr = 250
SI for 3 yearss = 250×3 = 750
P = A - SI
= 1500 - 750 = 750
SI = (P×N×R)/100
∴ R = (SI×100)/(P×N)
= (750×100)/(750×3) = 33.33%
Rate of interest = 33.33%

P + SI for 3 years = ₹ 8255 ……. (I)
P + SI for 5 years = ₹ 9425 …….(II)
From I and II
SI for 2 years = ₹ (9425 - 8255) = ₹ 1170
Then for 1 year = 1170/2 = 585
SI = ₹ 585
Sub SI = ₹ 585 in equ(I)
P + 585×3 = 8255
P = 8255 - 1755
= ₹ 6500
Rate for 1 year = (SI×100)/(6500×1)
= 9% per annum
The interest rate per annum = 9%

Given, principal = ₹ 450
S.I = ₹ 81
Rate of interest, r = 4.5 %
Let the time taken for an amount of ₹ 450 to yield ₹ 81 as interest = "n"
Simple interest, SI = (p×n×r)/100
⇒ n= SI × 100 / (p × r)
= (81 × 100 / 450×4.5 ) years
= 4 years
Thus, the time taken for an amount of ₹ 450 to yield ₹ 81 as interest = 4 years