The highest score in an innings was 3/11 of the total and the next highest was 3/11 of the remainder. If the scores differed by 9, then the total score is?

? Let the fraction = N
? (9 x N)/7 - (7 x N)/9 = 8/21
? (32 x N)/63 = 8/21
? N = (8/21) x (63/32) = 3/4
? Correct answer = N x 7/9 = 7/9 x 3/4 = 7/12

? 7/4 + 5/2 + 67/12 + 10 + 9/4 = (21 + 30 + 67 + 40 + 27/12) = 185/12

This is nearly greater than 15. Let required fraction be x.
Then, 185/12 - x = 15
? x = (185/12) - 15
= 5/12

? N x N x 1/N = 18²⁶/₂₇
? N³ = 512/27
? N³= (8/3)³
? N = 8/3 = 2²/₃

? 3N/4 - 3N/14 =150
? 15N/28 = 150
? N = (150 x 28) /15 = 280

? N x 17/8 - N x 8/17 =225
? 225 x N / 136 = 225
? N = (225 x 136) / 225 = 136

Let there be N members, other than father .
Father's share = 1/4, other's share = 3/4.
Each of other's share = 3/4N
? 3 x 3/4N = 1/4
? N = 9
Hence, the total number of members = N + 1 = 10

Suppose Ravi earns Rs. N in each of the 11 months.
Then earning in January = Rs. 2 x N.
? Total annual income = (11 x N + 2 x N) = Rs. 13 x N
Part of total earning in January = (2 x N) / (13 x N) = 2/13

(?)² = ?13² + 28 / 4 - (3)³ + 107
= ?169 + 7 - 27 + 107
= ?256
= ?16
= 4

We know that, (a + b)² = a² + b² + 2ab
= 234 + 2 x 108 = 450
(a - b)² = a² + b² - 2ab
= 234 - 2 x 108 = 18
? (a + b)²/(a - b)² = 450/18 = 25
? [(a + b)/(a - b)]² = 25
? (a + b)/(a - b) = ?25 = 5

a² + 1 = a
? a + 1/a = 1
On squaring both sides, we get
a² + 1/a² + 2 = 1
On cubing both sides, we get
(a² + 1/a²)³ = (-1)³
? a⁶ + 1/a⁶ + 3a² x 1/a² (a² + 1/a²) = -1
? a⁶ + 1/a⁶ + 3 x (-1) = -1
Now, a⁶ + 1/a⁶ + 1 = 3
As, a¹² + a⁶ + 1 can be written as a⁶ + 1/a⁶ + 1
? a¹² + a⁶ + 1 = 3