7
Q:

# A rectangular box measures internally 1.6m long, 1m broad and 60cm deep. The number of cubical box each of edge 20cm that can be packed inside the box is:

 A) 30 B) 60 C) 90 D) 120

Explanation:

Number of blocks =$\inline \fn_jvn \inline {\left ( \frac{160\times 100\times 60}{20\times 20\times 20} \right )}$=120

Q:

A single pipe of diameter x has to be replaced by six pipes of diameters 12 cm each. The pipes are used to covey some liquid in a laboratory. If the speed/flow of the liquid is maintained the same then the value of x is ?

 A) 14.69 cm B) 29.39 cm C) 18.65 cm D) 22.21 cm

Explanation:

Volume of water flowing through 1 pipe of diameter x = Volume discharged by 6 pipes of dia 12 cms

As speed is same, area of cross sections should be same.

Area of bigger pipe of diameter x = Total area of 6 smaller pipes of diameter 12

i.e $\inline&space;\dpi{80}&space;\fn_jvn&space;\small&space;\prod&space;R^{2}=6x\prod&space;R1^{2}$

Here R = R and R1 = 12/2 = 6

$\inline \dpi{100} \fn_jvn \small \Rightarrow R^{2} = 6x6x6$

R = 14.696

=> D = X = 14.696 x 2 = 29.3938 cm.

1 1
Q:

A store owner is packing books into larger boxes that measure 25 by 42 by 60 inches. If the measurement of each book is 7 by 6 by 5 inches, then how many books can be placed in the box ?

 A) 175 B) 345 C) 265 D) 300

Explanation:

Number of books that can be placed in the larger box is given by Volume of Box / Volume of book.
Now, n = 25 x 42 x 60 / 7 x 6 x 5
= 63000 / 210
= 300.
$\fn_jvn&space;\small&space;\therefore$  300 books can be in that box.

5 25
Q:

How many squares with sides 1/2 inch long are needed to cover a rectangle that is 4 ft long and 4 ft wide ?

 A) 9216 B) 10246 C) 12345 D) 7527

Explanation:

It takes four of those little squares -- each one 1/2 inch on a side -- to cover one square inch. That's because each one is 1/2 x 1/2, or 1/4 of a square inch.
In a rectangle that is 48 inches by 48 inches, there are 2304 square inches.(1 ft = 12 inches)
Since it takes 4 little squares to cover 1 sq inch, then it would need 2304 x 4 squares (1/2 inch on a side each) to cover a rectangle 4 feet by 4 feet.

That is 9,216 of those squares.

2 14
Q:

How many meshes are there in 1 squrare meter of wire gauge if each mesh is 8mm long and 5mm wide ?

 A) 2500 B) 25000 C) 12500 D) 15400

Explanation:

We know that,

One square meter is equal to 10,00,000 sq mm.
Given, each mesh is 8mm length and 5mm wide
Therefore for each mesh : 8 x 5 = 40 sq mm.
So, number of meshes= $\inline \fn_jvn \small \frac{1000000}{40}$ = 25000.

2 10
Q:

How many iron rods, each of length 7 mts and diameter 2 cms can be made out of 0.88 cubic metre of iron ?

 A) 500 B) 600 C) 400 D) 300

Explanation:

Given length of iron rod =7 mts

and diameter of rod = 2 cms

$\inline&space;\fn_jvn&space;\small&space;\Rightarrow&space;r&space;=&space;\frac{1}{100}&space;mts$

$\fn_jvn&space;\small&space;\therefore$ Volume of one rod = $\inline&space;\fn_jvn&space;\small&space;\prod&space;r^{2}h\Rightarrow&space;\left&space;(\frac{22}{7}\times&space;\frac{1}{100}&space;\times&space;\frac{1}{100}\times&space;7&space;\right&space;)$ cu. m = $\inline&space;\fn_jvn&space;\small&space;\frac{11}{5000}$ cu. m

Given volume of iron = 0.88 cu. m

$\fn_jvn&space;\small&space;\therefore$ Number of rods = $\inline&space;\fn_jvn&space;\small&space;\left&space;(&space;0.88\times&space;\frac{5000}{11}&space;\right&space;)$ = 400.