**Directions(1-5): **Find the value of the question mark in the following questions.

- ? = [((11)^2 + 21)- (64)] – 200
– 115– 100– 75– 98– 122Option E

? = [((11)^2 + 21)- (64)] – 200

=> ? = 121+21 – 64 – 200

=> ? = 142 – 264

=> ? = – 122 - 4432+ ? – 4862 = (27)^2 – 546
625458525600613Option E

4432+ ? – 4862 = (27)^2 – 546

=> ? – 430 = 729 – 546

=> ? – 430 = 183

=> ? = 613 - (3136)^1/2 + (?)^1/2 – (3721)^1/2 = (4225)^1/2 – (2809)^1/2
222250175289200Option D

(3136)^1/2 + (?)^1/2 – (3721)^1/2 = (4225)^1/2 – (2809)^1/2

=> 56 +(?)^1/2 – 61 = 65 – 53

=> ? = 289 - 1242/54 + 14^2 – 25% of 1640 = ? – 24% of 1625
162155180175199Option E

1242/54 + 14^2 – 25% of 1640 = ? – 24% of 1625

=> ? – 0.24*1625 = 23+196 – 410

=> ? – 390 = 219 – 410

=> ? = 199 - 11*13 + ?^2 – 10*12 = 15*18 – 83*2
98756Option A

11*13 + ?^2 – 10*12 = 15*18 – 83*2

=> 143 + ?^2 – 120 = 270 – 166

=> ?^2 + 23 = 104

=> ? = 9 - Present ages of Ram and Shyam are (x+3) and (2x+2) years resp. Present age of Gopal is 25% more than the present age of Shyam. Find the value of x, if the present age of Ram, Shyam and Gopal is 30 years.
1210151614Option C

Sum of the present ages = (x+3)+(2x+2)+2.5x+2.5 = 3*30

=> x = 15 - Arun invested Rs.16000 in a scheme offering 10% compound interest for three years compounded annually. Rita invested Rs. 21000 in a scheme offering 8% simple interest for three years. Find the difference in the interests earned by Arun and Rita.
Rs.240Rs.245Rs.256Rs.232Rs.200Option C

Interest earned by Arun and Rita = 16000{(1+0.10)^3 -1} and 21000*0.8*3

= Rs.5296 and Rs. 5040

Difference = Rs.256 - A boat can cover 42 km upstream and 72 km downstream in 8 hours. It can cover 56 km in still water in 4 hours. The upstream speed of the boat is what percentage less than the downstream speed of the boat if the speed of the stream is greater than 1.75 km/hr.
15%25%18%20%22%Option B

Speed of the boat in still water = 56/4 = 14 km/hr.

Let the speed of the stream be x kmhr. 42/(14-x)+72/(14+x) = 8

=> x = 2

Downstream speed = 16 km/hr. Upstream speed = 12km/hr.

Required% = (16-12)/16*100 = 25% - Pipes A and B alone can fill an empty tank in 1 hour 45 minutes and 2 hours resp. Pipe C alone can empty the full tank in 4 hours 40 minutes. Find the time taken to fill the empty tank if all the three pipes are opened simultaneously.
6070805040Option B

Time taken by A alone to fill the empty tank = 60+45 = 105 minutes

Time taken by B alone to fill the empty tank = 2*60 = 120 minutes

Time taken by C alone to fill the empty tank = 4*60+40 = 280 minutes

Let the capacity of the tank = LCM(105,120,280) = 840 litre

Quantity of water filled by Pipe A alone in one minute = 840/105 = 8 litres

Quantity of water filled by Pipe B alone in one minute = 840/120 = 7 litres

Quantity of water filled by Pipe C alone in one minute = 840/280 = 3 litres

Quantity of water filled by A,B and C alone in one minute = 8+7-3 = 12 litres

Total time taken by three pipes to fill the empty tank = 840/12 = 70 minutes - Average age the class of 45 students is 16 years. Average age of all the boys in the class 18 years six months and the average age of all the girls in the class is 14 years. The number of boys in class is how much percentage less/more than the number of girls in the class?
23%15%22%10%20%Option E

Let the number of boys in the class be x.

And the number of girls = (45-x)

Now, 18.5x + 630 – 14x = 720

=> x = 20

So, the number of boys and girls are 20 and 25 resp.

Required% = (25-20)/25*100 = 20%