  Important for :
1
Of three numbers, the sum of the first two is 45, the sum of the second and the third is 55, and the sum of the third and thrice the first is 90. Find the third number.
» Explain it
C
Let the number be x, y and z.

Then x + y = 45      ....(i)                y + z = 55     ....(ii)               z + 3x = 90    .... (iii)

Now, from (i)

y = 45 – x

And from (ii) z = 55 – y

∴     z = 55 – (45 – x)

z = 10 + x

Putting the value of z in equn. (iii) , we have

3x + 10 + x = 90

∴      x = 20

y = 45 – 20 = 25   and   z = 10 + 20 = 30.

Hence, option C is correct.

2
A social group named BACHPAN offers fruit to the orphans. Every orphan receives orange, Litchi and apple in the ratio 6 : 4 : 14 in terms of dozen but the weight of one Apple is 640 grams and weight of orange and Litchi is in the ratio of 2 : 6. The weight of one Orange is 160 grams. Find the ratio of the percentage contribution of all the fruits in terms of weight?
» Explain it
A
Ratio of fruits in terms of dozen = Orange: Litchi: Apple = 6 : 4 : 14

Ratio of per fruit in terms of weight = Orange: Litchi: Apple = 160 : 480 : 640

∴   Ratio of fruits (combined) in terms of weight (6 × 160) : (4 × 480) : (14 × 64)

⇒ 960 : 1920 : 8960
 % contribution of Orange = 960 × 100 = 8.1% 11840

 % contribution of Litchi = 1920 × 100 = 16.2% 11840

 % contribution of Apple = 8960 × 100 = 75.7% 11840

Hence correct option (A) is correct.

3
Two trains of same length are running in parallel tracks in the same direction with speed 60 km/hr and 90 km/hr respectively. The latter completely crosses the former in 30 seonds. The length of each train (in metres) is
» Explain it
A
When two trains cross each other, they cover distance equal to the sum of their lengths with relative speed.

Let's take length of each train = x, total length of both trains = 2x, Crossing time = 30 sec.

Relative speed = 90 – 60 = 30 km/hr

 = 30 × 5 = 25 m/sec. 18 3

Total length = Time × Relative speed

 ⇒   2x  = 30 × 25 ⇒ 10 × 25 = 125 m. 3 2

Hence, option A is correct.
4
The ratio of milk to water in three containers of equal capacity is 3 : 2, 7 : 3 and 11 : 4 respectively. The three containers are mixed together. What is the ratio of milk to water after mixing?
» Explain it
C
Let the capacity of each be ‘a’ litre

Then quantity of milk in container after mixing is

 ( 3 + 7 + 11 ) a 5 10 15

 = ( 3 × 6 + 7 × 3 + 11 × 2 ) a 30

 = ( 61 ) a 30

And  quantity of water in container after mixing is

 ( 2 + 3 + 4 ) a 5 10 15

 = ( 29 ) a 30

⇒ required  ratio of milk to water after mixing

 ( 61 ) a 30
= 61:29
 ( 29 ) a 30

Hence option C is correct.

5
A box contains 21 balls numbered 1 to 21. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls are even numbered?
» Explain it
C
There are 10 even numbers in the group 1-21.

 ∴   The probability that the first ball is even numbered = 10 21

Since the ball is not replaced there are now 20 balls left, of which 9 are even numbered.

 ∴ The probability that the second ball is even numbered = 9 20

 ∴   Required probability = 10 × 9 = 9 = 3 21 20 42 14

Hence, option C is correct.