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
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
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 number of bangles be x. Then, x - 38 is a perfect square and x + 25 is a perfect square.
Now, using the option, we find that x = 999
999 - 38 = 961 is a perfect square.
999 + 25 = 1024 is a perfect square
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
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 %
Let the CP be Rs. x , then SP be 0.96x
? 0.96x = 240
? x = 250
Now the new SP = 250 X 1.1 = 275
SP = 100/12 paise
Let's CP = x
SP = 0.8x = 100/12
? x = 10/(0.8x12) paise
Therefore, CP = 100/9.6 paise
Thus the new SP (with 20% profit) = 100/9.6 X 1.2 = 100/8 paise
Hence, 8 apples can be purchased for Rs.1 to gain 20%
6% of cost price (CP) = 1425 - 1353 = 72
? CP = ( 72 x 100 ) / 6 = 1200
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