57
Q:

# In three coloured boxes - Red, Green and Blue, 108 balls are placed. There are twice as many balls in the green and red boxes combined as there are in the blue box and twice as many in the blue box as there are in the red box. How many balls are there in the green box ?

 A) 18 B) 36 C) 45 D) None of these

Explanation:

Let R, G and B represent the number of balls in red, green and blue boxes respectively.

Then,

R + G + B = 108 ...(i),

G + R = 2B ...(ii)

B = 2R ...(iii)

From (ii) and (iii), we have G + R = 2x 2R = 4R or G = 3R.

Putting G = 3R and B = 2R in (i), we get:

R + 3R + 2R = 108 ${\color{Blue}&space;\Rightarrow&space;}$ 6R = 108 ${\color{Blue}&space;\Rightarrow&space;}$ R = 18.

Therefore Number of balls in green box = G = 3R = (3 x 18) = 54.

Q:

Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers ?

 A) 12 & 7 B) 13 & 8 C) 15 & 10 D) 14 & 9

Explanation:

x – y = 5

4x – 6y = 6

x = 12 y = 7

0 4
Q:

The arithmetic mean of the following numbers 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6 and 7, 7, 7, 7, 7, 7, 7 is   ?

 A) 6 B) 9 C) 7 D) 5

Explanation:

Arithmatic mean = sum/members

=> (1x1 + 2x2 + 3x3 + 4x4 + 5x5 + 6x6 + 7x7) / (1 + 2 + 3 + 4 + 5 + 6 + 7)

=> 140/28 = 5

1 23
Q:

Thrice the square of a natural number decreased by 4 times the number is equal to 50 more than the number. The number is  ?

 A) 5 B) 4 C) 7 D) 6

Explanation:

Let the number be x. Then,

$\inline \fn_jvn \small 3x^{2}$ - 4x = x + 50

$\inline \fn_jvn \small 3x^{2}$ - 5x - 50 = 0

(3x + 10)(x - 5) = 0

x = 5

1 15
Q:

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

 A) 30 B) 27 C) 23 D) 33

Explanation:

Then, A:B = 2:3 and B:C = 5:8
= (5 x 3/5) : (8 x 3/5) = 3:24/5
A:B:C = 2:3:24/5
= 10:15:24 => B = 98 x 15/49 = 30.

3 44
Q:

Ajay and Vijay have some marbles with them. Ajay told Vijay "if you give me 'x' marbles, both of us will have equal number of marbles". Vijay then told Ajay "if you give me twice as many marbles, I will have 30 more marbles than you would". Find 'x'  ?

 A) 4 B) 10 C) 8 D) 5

Explanation:

If Vijay gives 'x' marbles to Ajay then Vijay and Ajay would have V - x and A + x marbles.
V - x = A + x --- (1)
If Ajay gives 2x marbles to Vijay then Ajay and Vijay would have A - 2x and V + 2x marbles.
V + 2x - (A - 2x) = 30 => V - A + 4x = 30 --- (2)
From (1) we have V - A = 2x
Substituting V - A = 2x in (2)
6x = 30 => x = 5.