Quantitative Aptitude - Arithmetic Ability Questions

Number of square units in 13 by 9 is given by the area it forms with length and breadth as 13 & 9

Area = 13 x 9 = 117

Hence, number of square units in 13 by 9 is 117 sq.units.

Let l, b the sides of the base, so that the area of the base = lb
remains constant.
Let ‘h’ be the height of the solid.
Volume of the solid, V = l× b× h.
Since the volume is to be increased by 50%

Let the average bill paid by twenty members = 'x'

But 19 men paid each = Rs. 70

20th man paid Rs. 90.25 more than the avg bill of 20 = x + 90.25

20x = 19(70) + x + 90.25
19x = 1330 + 90.25
19x = 1420.25
x = 1420.25/19 = Rs. 74.75

But the total bill = 20 x 74.75 = Rs. 1495.

Let number of boys in the school = x

Let number of girls in the school = y

Number of students participated in the sports = 300

Out of which boys = 100

but given number of boys participated in sports = x/3

=> x/3 = 100

=> x = 300

Remaining girls = 300 - 100 = 200

=> y/2 = 200

=> y = 400

Therefore, total number of students in the school = x + y = 300 + 400 = 700

Let the avg age of 7 boys be 'p' years
Let the age of the girl be 'q' years
From given data,
The age of 7 boys = 7p years
Now the new average = (p + 1) when 22 yrs is replaced by q
Now the age of all 7 will become = 7(p + 1) yrs
Hence, 7p - 22 + q = 7(p + 1) yrs
7p - 22 + q = 7p + 7
q = 22 + 7 = 29

Therefore, the age of girl = q = 29 years.

Here total parts of milk and water in the solution is 6+2 = 8 parts.

1part = 640/8 = 80

old mixture contains 6parts of milk and 2 parts of water(6:2).

To get new mixture containing half milk and half water, add 4parts of water to the old mixture then 6:(2+4) to make the ratio same.

i.e, 4 x 80 = 320 ml.

The 8 letters can be written in 8! ways.
n(S) = 8!
Let E be the event that the letters b,c,d,e always come together when the first 8 alphabets are written down.
Now the letters a, (bcde), f, g and h can be arranged in 5! ways.
The letters b,c,d and e can be arranged themselves in 4! ways.
n(E) = 5! x 4!
Now, the required P(E) = n(E)/n(S) = 5! x 4!/8! = 1/14
Hence the answer is 1/14.