The pattern is 23, 33, 43, 53, 63, 73.
But 100 is not a perfect cube
In each number except 751, the difference of third and first digit is the middle one .
Let the cost price of first bicycle be ? P.
Then, the cost price of second bicycle = ? (1600 - P)
According to the given condition,
[20% of P + 10% of (1600 - P )] - [10% of P + 20% of (1600 - P)] = 5
? [(20P/100) + [10 x (1600 - P)]/100] - [(10P/100) + {20 x (1600 - P)}/100] = 5
? (P/5 + (1600 - P)/10) - (P/10 + (1600 - P)/5) = 5
? P/5 - P/10 + (1600 - P)/10 - (1600 - P)/5 = 5
? 2P = 1600 + 50
? P = 1650/2 = 825
? Cost of second bicycle = (1600 - 825) = ? 775
? Required difference = 825 - 775 = ? 50
Let the cost price of table = ? N
Then, selling price with 15% gain
= (100 + Gain%) x CP/100
= (100 + 15)% x CP/100
= (115 x N)/100 = ? 115N/100
Now CP = [(100 - 25%) x CP]/100 = ? 75N/100
New SP = ? (115N/100) - 60
Now, according to the question,
[[(115/100 )- 60) - (75N/100)]/ (75N/100)] x 100 = 32
? [[(115N - 6000 - 75N)/100 ]/ (75N/100)] x 100 = 32
? [(40N - 6000)/75N] x 100 =32
? (40N - 6000)/(3N x 4) = 32
? 160N - 24000 = 96N
? 160N - 96N = 24000
? 64N = 24000
? N = 24000/64
? N = ? 375
? The cost price of table is ? 375.
By hit and trial ,
Case I t = ? 400 and q = 20 unit
Then, from option (a),
Total profit = 600q - 5t
= 600 x 20 - 5 x 400
= 12000 - 2000 = ? 10000
Case II t ? 600 and q = 25 units
Total profit = 600q - 5t
= 600 x 25 - 5 x 600
= 600(25 - 5)
= 600 x 20
= ? 12000
Let CP = N
Then, SP = 110N / 100 = ? 11N/10
Now, CP = 96% of N = 96N/100 = ? 24N/25
Now, according to the question,
SP = ? (11N/10) + 6
? (11N/10) + 6 = 1183/4% of 24N/25
? (11N + 60)/10 = (475/400) x (24N/25) = 57N/50
? 550N + 3000 = 570N
? 20N = 3000
? N = 3000/20 = 150
? CP = ? 150
The pattern is 12, 22, 32, 42, 52, 62, 72 .
But, instead of 52, It is 20, which is to be turned out.
Each of the number except 54, is a multiple of 5.
Each of the number except 72, is a perfect square.
Each of the number except 28, is a multiple of 3.
Each of the given number is except 23, is perfect square
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