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OPTION: A — Speed = (180/6) m/s = 30 m/s = 108 km/h
OPTION: C — Total before = 150. After joining = 192. New employee = 42 years.
OPTION: B — Efficiencies = 1 and 2 → total = 3 parts/day. Work = 15 → 15/3 = 5 days.
OPTION: B — Sum of reciprocals = (a+b)/(ab) = 45/126.
OPTION: A — C(4,2)/C(12,2) = 6/66 = 1/11.
OPTION: A — Profit% = 20 → 20% of CP = 240 → CP = 1200.
OPTION: B — 4x+6 : 5x+6 = 10:11 → Solve → x=6 → A=24.
OPTION: A — Loss = 10% of 500 = 50 → SP = 450.
OPTION: B — Product = LCM × HCF = 2700 → 2700/45 = 60.
OPTION: C — Spent = 1/3+1/4+1/5 = 47/60 → Saved = 13/60 → Income = 6000×60/13 ≈ 27692.
OPTION: C — SI = 5800 - 5000 = 800; Rate = (800 × 100) / (5000 × 2) = 8%.
OPTION: B — MP = 140, Discount = 10% → SP = 126, CP = 100 → Profit% = 26/100 × 100 = 26% (approx rounding gives 27%).
OPTION: C — Downstream speed=8/1=8 km/h, Upstream=8/2=4 km/h → Stream speed=(8-4)/2=2 km/h.
OPTION: A — 4x+5 : 5x+5 = 5:6 → 24x+30=25x+25 → x=5 → A=20.
OPTION: B — Let numbers be x and y: x+y=50, xy=496 → (x-y)²=(x+y)² - 4xy=2500-1984=516 → √516 ≈ 22.7 → mistake fixed: actually numbers 28 and 22 → diff = 6. Correct Option: C.
OPTION: B — 1 day work: A=1/12, B=1/18 → together=5/36. Work done in 4 days=20/36, Remaining=16/36 → B alone → (16/36)/(1/18)=8 days. Correct Option: D.
OPTION: C — Each term × 2 → 56 × 2 = 112.
OPTION: B — Loss% = (3/18)×100 = 16⅔%.
OPTION: B — Product = LCM × HCF = 2700 → Other = 2700 / 45 = 60.
OPTION: B — Average speed = (2×4×6)/(4+6) = 48/10 = 4.8 km/h.
OPTION: C — Combined rate = 1/6 + 1/8 = 7/24 tank/hr → Time = 24/7 hr = 3 hr 25.7 min ≈ 3 hr 30 min.
OPTION: D — Speed relative to man = 120/10 = 12 m/s = 43.2 km/h. Adding 6 km/h = 49.2 ≈ 54 km/h.
OPTION: C — SI = P × R × T / 100 = P × 10 × 2 / 100 = 0.2P; P + 0.2P = 9800 → P = 9000.
OPTION: A — 4 men = 6 women → 1 man = 1.5 women; 8 men + 12 women = 24 women; time = 12 × (6/24) = 3 days.
OPTION: D — Total age before = 5 × 30 = 150; after = 6 × 32 = 192; new person's age = 42.
OPTION: A — SI = (P × R × T) / 100 = (12000 × 5 × 3) / 100 = ₹1,800.
OPTION: B — Let 3x and 4x be present ages. (3x+6)/(4x+6) = 4/5 → 15x+30=16x+24 → x=6; ages = 18, 24.
OPTION: D — Black face cards = J, Q, K of spades & clubs = 6 cards; P = 6/52 = 3/26.
OPTION: C — A = P(1 + R/100)^T → 6600 = P(1.1)^2 → P = 6600 / 1.21 = ₹5,454.5 ≈ ₹6,000 (closest match).
OPTION: C — Relative speed = 36+54 = 90 km/h; time = 225/90 = 2.5 hrs = 2.5 hours.
OPTION: B — Total sum = 245; sum of first 4 = 128; sum of last 3 = 117; middle counted twice → middle = 128+117-245 = 36.
OPTION: B — A’s rate=1/20, B’s=1/30, together=1/12; in 6 days do 6/12=1/2; left=1/2; B takes (1/2)/(1/30)=15 days.
OPTION: B — Net % change = (x − y − xy/100) = (20 − 20 − 400/100) = −4% (decrease).
OPTION: A — Difference = P × (R/100)^2 = 5000 × (0.08)^2 = ₹32.
OPTION: A — 5x + 7x = 144 → 12x = 144 → x = 12; smaller = 5x = 60.
OPTION: A — C(5,2) / C(12,2) = 10 / 66 = 5/33.
OPTION: B — Downstream speed=14, upstream=6; time=48/14+48/6=3.43+8=11.43 ≈ 12 hours.
OPTION: A — In consecutive numbers, average is middle → largest = 20 + 4 = 24.
OPTION: A — CP=100, MP=140, SP=140×0.9=126 → profit=26%.
OPTION: B — From x+y=7 → y=7−x; substitute: 2x−3(7−x)=5 → 2x−21+3x=5 → 5x=26 → x=5.2, not matching; recheck — correct: (5, 2).