Solution:Logic for series I:
22 + 6 × 1 = 28
28 + 6 × 2 = 40
40 + 6 × 3 = 58
58 + 6 × 4 = 82
82 + 6 × 5 = 112
So, wrong term = P = 80, S = 82
Logic for series II:
156 − 11 = 145
145 − 13 = 132
132 − 17 = 115
115 − 19 = 96
96 − 23 = 73
So, wrong term = Q = 130, T = 132
Logic for series III:
13 + 2² = 17
17 + 4² = 33
33 + 6² = 69
69 + 8² = 133
133 + 10² = 233
So, wrong term = R = 135, U = 133
A shopkeeper bought two items A and B at Rs.4000 together.
Cost price of item A = Rs. a
Then, cost price of item B = Rs. (4000 − a)
He marked item A at (P/2)% above its cost price and item B at (R − P)% above its cost price.
P/2 = 80/2 = 40
R − P = 135 − 80 = 55
Now, marked price of item A = (100 + 40)% of a
= 1.4a
Marked price of items B = (100 + 55)% of (4000 − a)
= 6200 − 1.55a
Now, total marked price = 1.4a + 6200 − 1.55a
= 6200 − 0.15a
After allowing [(Q − P)/2]% discount on both the items together, he sold them together at Rs.4537.5.
(Q − P)/2 = (130 − 80)/2 = 25
Then, total selling price = (100 − 25)% of (6200 − 0.15a)
= (3/4) × (6200 − 0.15a)
Now, 4537.5 = (3/4) × (6200 − 0.15a)
6050 = 6200 − 0.15a
0.15a = 150
a = 1000
From (i): Now, 8U = 8 × 133 = 1064 > a
So, statement (i) is not correct.
From (ii): 20S = 20 × 82 = 1640
15T = 15 × 132 = 1980
20S > a, 15T > a
So, statement (ii) is not correct.
From (iii): 4(T + U) = 4(132 + 133) = 1060
Then, a < 1060
So, statement (iii) is correct.