The compound interest on a certain sum for 2 years at 10% per annum is Rs. 1155. The simple interest on the same sum for double the time at half the rate percent per annum is ?

Let first number = P
And second number = Q
According to the question
P - Q = 10 ....(i)
And 3P - 4Q = 18...(ii)

on multiply eq (i) by 3 and then subtract eq (ii) from it
3P - 3Q = 54
3P - 4Q = 18
Q = 36

On putting the value of Q in the eq (i)
P = 18 + Q = 18 +36
? P = 54
Required sum = P + Q = 54 +36 =90

Let their radii be x and 2x .
Ratio of their surface areas = [4?x²]/[4?(2x)²] = 1/4 = 1 : 4

Given, Investment of B = 1/6 of total capital
? Investments of A and C each = 1/2(1 - 1/6) of total capital
= (1/2) x (5/6) of total capital
= (5/12) of total capital

Now. A's share : B's share : C's share = (5/12) : (1/6) : (5/12) = 5 : 2 : 5
Let A's share = 5N
B's share = 2N
C's share = 5N

According to the question.
5N + 2N + 5N = 33600
? 12N = 33600
? N = 33600/12 = 2800
? Difference in the profits of B and C
= 5N - 2N = 3N = 3 x 2800 = ? 8400

According to the formula,
Annual payment = 100P / [100 x T + {RT (T - 1)/2}]
= (1092 x 100) / [100 x 2 + {24 (2 - 1)/2}]
= (1092 x 100)/2012
= ? 515.09
? ? 515

?4/?3 - ?3/?4
= 2/?3 - ?3/2
= (4 - 3)/2?3
= 1/2?3

Since minute hand gains 5 minutes in every 60 minutes
⇒ second hand gains 5 seconds in every 60 seconds
∴ In every 60 seconds true time, it moves 65 seconds
⇒ 65 × 6° = 390°.
Hence , required answer will be 390° .

Let breadth = L meters. Then, height = 5L meters and length = 40L meters
? L x 5L x 40L = 12.8
? L³ = 12.8/200 = 128/2000 = 64/1000
? L = 4/10
Thus, breadth = (4/10) m = (4 x 100)/10 cm = 40 cm

Let total number of employee be 100.
? Number of men = 60% of 100 = 60
and number of women = 40% of 100 = 40
Number of men drawing more than ? 50000 = 40% of 60 = 24 men
Since, number of total employees drawing more than ? 50000 = 36% of 100 = 36
Number of women who more than ? 50000 = 36 - 24 = 12
Number of women who draw less than ? 50000 = 40 - 12 = 28
Percentage of women who draw less then ? 50000 per year = (28 x 100)/40 = 70%

Let usual speed and usual time taken by the jogger are D and T, respectively.
Let his new speed be D'. Then,
DT = (3D'/4)T
? D = 3D'/4
? D' = 4D/3

Thus, he has to increased his speed by
[(4D/3 - D) / D] x 100% .
= 33¹/₃ %

Let the original price be ? N per kg.
New price per kg = 60% of N = 3N/5
? 120 / (3N/5) - 120/N = 32
? 600/3N - 120/N = 32
? 200/N - 120/N = 32
? 80/N = 32
? N = 80/32 = 2.5
So, the original price is ? 2.50