The principle on which a simple interest of ? 55 will be obtained after 9 months at the rate of 3 ²/ ₃% per annum is

Let principal = P, time = T and rate = T
According to the question,
(P x T x T) / 100 = P/16 [? time and rate are equal]
? T² = 100/16
or T = 10/4 = 5/2 = 2¹/₂ %

Let the principal be P.
Then, according to the question,
(P x T x T) / 100 = P/144 [? time and rate are equal]
? T² = 100/144
? T = 10/12 = 5/6 %

Given. T₁ = 2 yr and T₂ = 4 yr,
P₁ = 600, P₂ = 150.

According to the question,
SI₁ + SI₂ = 80
[(600 x R x 2)/100] + [(150 x R x 4)/100] = 80
? 120R + 60R = 800
? 180R = 800
? R = 800/180 = 80/18 = 40/9
= 4⁴/₉%

Given, T₁ = 5 yr, R₁ = 10% and
T₂ = 10 yr, R₂ = 8%
Let the first part = P
Then, second part = (1521 - P)

Now, according to the question.
[(P x 5 x 10)/100] = [{(1521 - P) x 10 x 8}/100]
? 5P = 12168 - 8P
? 13P = 12168
? P = ? 936

So second part = 1521 - 936 = ? 585

Given, R₁ = 6% R₂ = 10%
According to the question,
800 + [(800 x 6 x T)/100] = 600 + [(600 x 10 x T)/100]
800 + 48T = 600 + 60T
? 12T = 200
? 3T = 50
? T = 50/3 = 16²/₃ yr

According to the question,
SI for 5 yr = ? 200
? Total SI for 10 yr = 200 + 600 = ? 800
When principal is trebled, then SI for 5 yr will also be treble and hence
SI for next 5 yr will be ? (200 x 3) i.e., ? 600.

Investment of Ramesh = 10% of 10000 = ? 1000
After 3 yr = 2500 - 1000 = ? 1500

We know.
SI = (P x R x T)/100
? 1500 = (1000 x R x 3)/100
? R = (1500 x 100) / (1000 x 3) = 50%
? 4 times of 50% = 200%

If the principal = P and interest = R%
Then, required ratio = [(P x R x 12)/100] / [(P x R x 18)/100]
= 12 / 18
= 2/3
= 2 : 3

Let the money at 10% be Rs. P, Then the money at 9% is Rs. (2600 - P )
? (P x 10 x 5)/100 = [(2600 - P ) x 9 x 6]/100
or 104 x P = 2600 x 54
or P = (2600 x 54) / 104 = Rs.1350

Let principle = P, then SI = (9/16) x P.
Let rate = R% per annum and time = R years
Then, 9/16 P = P x R x R / 100
? R² = 900/16
? R = 30/4 = 7¹/₂ years