In a bangel shop, the shopkeeper displays the bangels in the form of a square, then he is left with 38 bangles with him. If he wants to increse the size of square by one unit each side of the square, he found that 25 bangles fall short of in completing the square. The actual number of bangles which he had with him in the shop was?

7777 - N must be a perfect square.
Now, using the option, we find that N = 33
7777 - 33 = 7744 is perfect square.

Ans. LCM of 21, 36 and 66 = 2772
Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11
To make it a perfect square, it must be multiplied by 77 [for (7 x 11)].
? Required number = 2² x 3² x 7² x 11² = 213444

xy = [(?2 + 1)/(?2 - 1)] x [(?2 - 1)/(?2 + 1)] = 1
? 3(xy + 1) = 3(1 + 1) = 6
Now, x + y = [(?2 + 1)/(?2 - 1)] + [(?2 - 1)/(?2 + 1)]
= (?2 + 1)² + (?2 - 1)² / (?2 - 1) (?2 + 1)
= (2 + 1 +2?2) + (2 + 1 - 2?2) / (2 - 1) = 6
? 3(xy + 1) = x + y

Total collected amount = Rs. 29791
? Total number of student = ?29791 = 31

Let the total number of subbscribers be x.
Then, x² = 2582449
? x = ?2582449 = 1607

Let the number be x and y.
Now, according to the question,
x(x + y) = 2418 .....(i)
and y(x + y) = 3666 .....(ii)
On adding Eqs. (i) and (ii), we get
x² + xy + yx + y² = 6084
? x² + 2xy + y² = 6084
? (x + y)² = 6084
? x + y = ?6084 = 78
On subtracting Eq. (ii) from Eq. (i), we get
x² + xy - yx - y² = -1248
? x² - y² = -1248
? (x + y) (x - y) = -1248
? 78(x - y) = -1248
? x - y = - 1248 / 78 = -16
? (y - x) = 16

Let the total number of camels be x.
Then, acording to the question,
x/4 + 2?x + 15 = x
? x - x/4 - 2 ?x = 15
? 3x - 8?x - 60 = 0
? ?x = [8 ± ?64 + 720] / 6
= (8 ± 28) / 6
? x = 36

Cost of 15 eggs = 75 rupees
Cost of 1 egg = 75/15 = 5 rupees,
Cost of 5 dozens, i.e. 5 x 12 = 60 x 5 = 300

Each dozen carries cost 75 rupees and are sold for
12 x 15 = 180 rupees
profit = SP-CP
profit = 180-75 = 105 rupees

From question CP/SP = 12/18 = 2/3
? Profit (%) = ( 3 - 2 ) / 2 x 100 = 50%

2nd Solution:
CP = 100/18 = 5.55 paisa
SP = 100/12 = 8.33 paisa
? Profit = (8.33-5.55)/5.55 x 100 = 50 %