161. Read the information given below and answer the questions that follow.

X%y= (y

^{2}-x^{3})
X&y=(x

^{2}-y^{3})+(x%y)
f(a)=(a

^{2}+a^{3})
what is the value of ((x%y) – (x&y) ) (x%y)

^{-1}where x=2, y=1 ?
(a) 11/7 (b) -3/7 (c) 3/7 (d) -11/7

Solution: 3/7

162. The sum of three numbers is 98. If the ratio of first to second is 2:3 and that of the second to the third is 5:8 then the second number is :

Solution: a+b+c=98 à (1)

a/b=2/3 à a=(2/3)b à (2)

b/c=5/8 à c= (8/5)b à (3)

Substitute equations (2) and (3) in Equation(1)

b=30

**The basic fuel expenditure of a country is dominated by four major uses - Domestic, Transport, Industry and Electricity. In 2014, the total amount of energy used was equivalent to 600 million tonnes of coal. Directions: Study the following graph carefully & answer the questions given below it.**

163. The central angle for the energy consumed for others is

a. 12 b. 15 c. 18 d. 9

Ans: 100 % it is 360

Then 5% is = (360/100)*5 = 18

164. What is difference between energy used for domestic and others in the country in 2014?

a. 18 million b. 54 million c. 48 million d. 32 million

Ans: 13% - 5% = 8% of 600 Million tonnes

48 million

165. If the energy requirement of transport in 2014 were 220 million tonnes, the approximate amount of additional primary energy required would be

a. 400 million tonnes of coal b. 750 million tonnes of coal

c. 890 million tonnes of coal d. 1000 million tonnes of coal

Ans: let’s say total primary energy is x

Then 22% of x = 220

(22/100) * x = 220

X=1000

Ans: 1000-600 = 400

166. If the simple interest on a certain sum of money for 8 months at 8%p.a exceeds the simple interest on the same sum for 12 months at 5% p.a by Rs. 20, then find the value of sum.

Solution:

(P*8*8)/(12*100) - (p*1*5)/100 = 20

P=6000

167. If m= 3-2√2, then the value of √m – (1/√m) is:

Solution:

Let’s say √m – (1/√m) = x

Squaring on both sides

m+1/m-2 = x

^{2}
if m= 3-2√2, then 1/m = 3+2√2

so m+1/m-2=x

^{2}
4=x

^{2}
X=2

Ans:2

168.

A mixture of 66 litres contains whisky and water in the ratio 4:7 how many litres of whisky and water each must be added to the mixture to make the ratio 2:3?

A mixture of 66 litres contains whisky and water in the ratio 4:7 how many litres of whisky and water each must be added to the mixture to make the ratio 2:3?

Solution:

Quantity of whisky in 66 litres mixture is : (4/11)*66 = 24

Similarly quantity of water in 66 litres mixture is : (7/11)*66= 42

Let’s say adding x litres of whisky and water added to make mixture ratio as 2:3

Then (24+x)/(42+x)= 2:3

X=12

169. Two cities x and y are 400km apart. Q leaves x 8 hours after P. Both P and Q arrive simultaneously. Find the time the slower person spent on the trip if the speed of one of them was 15kmph higher than that of other?

Ans: Ans: 19.14 hrs.

Let speed of P = p kmph, then speed of Q=(p+15) kmph.

Let slower person P takes 't' hrs. then Q takes (t-8) hrs. to reach y

We have, pt = (p+15)(t-8)

=> 8p - 15t + 120 = 0

As p=400/t, substituting in above equation, 8x(400/t) -15t + 120 = 0

=> 3t² - 24t - 640 = 0

On solving t=19.14

Let speed of P = p kmph, then speed of Q=(p+15) kmph.

Let slower person P takes 't' hrs. then Q takes (t-8) hrs. to reach y

We have, pt = (p+15)(t-8)

=> 8p - 15t + 120 = 0

As p=400/t, substituting in above equation, 8x(400/t) -15t + 120 = 0

=> 3t² - 24t - 640 = 0

On solving t=19.14

170. Train ‘A’ leaves a source station for destination station at 11 a.m., running at the speed of 60 kmph. Train B leaves the same source station to the same destination by the same route at 2 p.m. on the same day, running at the speed of 72 kmph. At what time will the two trains meet each other?

Solution:

With 60 kmph in 3 hours train ‘A’ covers 180 kms.

Train B speed is 12kmph more than train ‘A’. Because train B started 3 hours later so it has to cover 180 extra with extra 12kmph speed.

Time taken is = 180/12 = 15 hours

So 15 hours from 2p.m is

**5a.m on the next day**
171. A motor cycle is moving with the speed of 47.52 kmph and the radius of the wheel of the motorcycle is 21cm. calculate the approximate number of revolutions made by the wheel in one minute.

Solution:

Ans:600

172. A wire of legth 5 cm is subjected to stress that leads to the increase in its length by 25.60%. If the wire is re-shaped into a circle by joining its both ends, then what will be the radius of the circle?

Ans: 1 cm

173. If the length of a rectangle is thrice its width and it is known that length of its diagonal is 15√10 cm. then determine the area of the rectangle.

Ans: 675

174. A boy buys a pen for Rs. 25 and sells it for Rs. 20. Find his loss percent.

Ans: 20

175. A and B are running at 250 m/minute and 300 m/minute, in the same direction. The distance between the two, after 1 hour, will be:

Ans: 3 km

176. A number when divided by 2, 3, 4, 5 and 6 leaves a remainder 1 in each case but it is exactly divisible by 7.

a. 305 b. 606 c. 601 d. 301

Ans: 301

Solution: find lcm of (2,3,4,5 and 6) = 60

Divide given options with 60 remainder should be 1.

Option c and d satisfy above conditions.

Divide c and d options with 7 . only option(d) is divisible with 7.

177. If (m – m

^{-1})= 1/5, then determine the value of ( 25m^{2}+ 25m^{-2}).
a. 2 b. 1 c. 49/25 d. 51

Ans: 51.

Solution: (m – m

^{-1})= 1/5
Squaring on both sides

m

^{2}+1/m^{2}-2=1/25
m

^{2}+1/m^{2}=51/25
Substitute above value

25(m

^{2}+m^{-2})= 51.
178. The ratio between the speeds of two trains is 15:13. If the second train runs 260 km in 2 hours, then the speed of the first train is

a. 75 kmph b. 150 kmph c. 120 kmph d. 90 kmph

Ans: 150 kmph

Solution: s1/s2= 15/13

S2=130 kmph ( given)

So s1= 150 kmph

179. Find the value of “x” if 10/3 : x :: 5/2 : 5/4

a. 2/5 b. 5/3 c. 1/5 d. 3/5

Ans: 5/3

180. Fredy drives his car on two journeys the first journey is of 8 miles and takes 35 minutes, while the second journey takes 17.5 miles and takes 55 minutes. Find the average speed of the two journeys combined.

a. 17 miles per hour b. 20 miles per hour c. 15 miles per hour d. 25 miles per hour

Ans: 17 miles per hour

Solution: Average Speed = Total distance/ Total time

= (8+17.5)/ (35+55)/60= 17 miles per hour ( convert time in minutes to hour )