The correct answer is option 1 i.e. 414.

Three pipes A, B, and C can fill a cistern in 138 hours

Total work = worker × efficiency

According to the question

⇒ 138 × (A + B + C) = 46 × (A + B + C) + 138 × (A + B)

⇒ 92 × (A + B + C) = 138 × (A + B)

⇒ 92 C = 46 × (A + B)

⇒ C/(A + B) = 1/2

⇒ So, C/(A + B + C) = 1/3

Total capacity of tank = 3 × 138 = 414 units

Hence, the time taken by C alone to fill the tank = 414/1 = 414 hours

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

Arvind works 4 times as fast as Suresh.

Time taken by Suresh = 20 days

⇒ Total work = Efficiency × Time

Let the efficiency of Suresh be 1 unit/day

⇒ Efficiency of Arvind = 4 unit/day

⇒ Total work = 1 × 20 = 20 units

Work done by Arvind and Suresh in a day = 4 + 1 = 5 units

Time taken by Arvind and Suresh to complete the same work = 20/(4 + 1) = 20/5 = 4 days.

The correct answer is Option 1 i.e. 11.11%.

Let Cost price = 100

Marked price = 100 + 20% of 100 = 120

Discount per cent = 25%

Selling price = (100 - 25) % of 120 = 90

Selling price for no profit, no loss = 100

Increase required = 100 - 90 = 10

Hence,

Percentage increase = (10/90) × 100 = 11.11%

The correct answer is option 3 i.e. 32.

Speed = Distance/time

In the first 25 minutes, he travelled the distance with a speed of 15.2 m/s = 25 × 60 × 15.2 = 22800 meters = 22.8 km

The remaining distance = 90 km - 22.8 km = 67.2 km

Hence, this distance covered by him in 35 minutes with a speed of = 67.2/35 × (1000/60) = 32 meters/second

The Correct answer is Option 3 i.e. 85.

Average = Sum of observations/Number of observations

Sum of 29 observations = 29 × 40 = 1160

Sum of first 15 observations = 15 × 38 = 570

Sum of last 15 observations = 15 × 45 = 675

Hence, 15th observation will be = (570 + 675) - 1160

⇒ 1245 - 1160 = 85

The correct answer is Option 3 i.e. ₹6991.

Let the sale for the 6th week be Rs. x

Average = Sum of observations/Number of observations

Now,

⇒ 8500 = (8435 + 8927 + 8855 + 9230 + 8562 + x)/6

⇒ 8500 × 6 = 44009 + x

⇒ 51000 = 44009 + x

⇒ x = 51000 - 44009

⇒ x = 6991

Hence, the sale required for the 6th week is Rs 6,991

The correct answer is option 2 i.e. 12.5%

Profit = Selling price - Cost price

Profit% = (Profit/Cost price)

According to the question;

⇒ Selling price = 9 × (Selling price - Cost price)

⇒ SP = 9SP - 9CP

⇒ 9 CP = 8 SP

⇒ CP/SP = 8/9

Let the CP and SP be 8x and 9x.

Profit = 9x - 8x = x

Required profit percentage = (x/8x) × 100 = 12.5%

The correct answer is Option 4 i.e. 35.2 km/h.

Distance covered by John = 1000 m

Distance covered by Khan = 1000 - 120 = 880 m

Speed of John = 40 km/hr = 40 × 5/18 = (20 × 5)/9 = 100/9 m/sec

Time taken by John = 1000/(100/9) = 90 sec

Speed of John = (880/990) × 18/5 = 35.2 km/hr.