The correct answer is option 2 i.e. 1 : 6.

⇒ 58% of 182/(87% of 728)

⇒ (58/100) × 182/(87/100) × 728

⇒ (58 × 182)/(87 × 728)

⇒ (2/3) × (1/4)

⇒ 1/6 = 1 : 6

The correct answer is Option 1 i.e. Rs. 3003.6.

Calculations:

Rate = 9.7%

Time = 5 years

Simple Interest (S.I.) = PRT/100 = Rs. 1456.75

⇒ PRT/100 = 1456.75

⇒ P × (9.7) × (5)/100 = 1456.75

⇒ 48.5P = 145675

Principal (P) = 145675/48.5 = Rs. 3003.6

The correct answer is Option 4 i.e. 66.67%.

Percentage of Supervisors =  (Total number of Supervisors in a company/total number of Labourers) × 100

Tech M

Total number of Supervisors = 800

Total number of Labours = 1200

Percentage of Supervisors = (800/1200) × 100 = 66.67%

The correct answer is option 4 i.e. Rs. 69.

Selling price of 1 m cloth = 7565/85 = Rs. 89

Cost price = selling price - profit 

So, cost price = 89 - 20 = Rs. 69

The correct answer is Option 3 i.e. (a/100) % of x².

x% of a = b

∴ x/100 × a = b

b = xa/100

b% of x = b/100 × x

⇒ (xa/100)/100 × x

⇒ (a/100)/100 × x²

⇒ (a/100) % of x²

The correct answer is option 4 i.e 1441440.

⇒ 132 = 2² × 3 × 11

⇒ 156 = 2² × 3 × 13

⇒ 288 = 2⁵ × 3²

⇒ 12 = 2² × 3 

⇒ 840 = 2³ × 3 × 5 × 7

⇒ 624 = 2⁴ × 3 × 13

LCM of 132, 156, 288, 12, 840, and 624 = 2⁵ × 3² × 5 × 7 × 11 × 13 = 1441440

The correct answer is option 2 i.e. 60/11 days.

If two workers can do work in X days and Y days respectively.

X and Y together can complete the work = (XY)/(X + Y) days

Required number of days = (10 × 12)/(10 + 12) = 120/22 = 60/11 days

The correct answer is option 1 i.e. 132 km/hr. 

Speed = Distance/Time

Speed of the train = 550/15 m/sec

Speed of the train = (550/15) × (18/5) km/hr = 132 km/hr

The correct answer is option 3 i.e. 221.

Let's assume x is the fourth proportion of 189, 273, and 153.

189 : 273 :: 153 : x

⇒ 189x = 273 × 153

⇒ x = (273 × 153)/189

⇒ x = 221

The correct answer is option 2 i.e. 20%

Simple interest = (principal × rate of interest × time)/100

⇒ 900 = (1500 × r × 3)/100

⇒ r = 20%