Quantitative Aptitude - Arithmetic Ability Questions

Let original Cost price is x
Its Selling price = (105/100) * x = 21x/20
New Cost price  = (95/100) * x  = 19x/20
New Selling price = (110/100 )* (19x/20 )= 209x/200
[(21x/20) - (209x/200)] = 1
=> x = 200

1/8 - 1/x = 1/10

 => x = 40 hrs

Since their HCFs are 7, numbers are divisible by 7 and are of the form 7x and 7y

Difference = 14
=> 7x - 7y = 14
=> x - y = 2

product of numbers = product of their hcf and lcm
=> 7x * 7y = 441 * 7
=> x * y = 63

Now, we have
x * y = 63 , x - y = 2
=> x = 9 , y = 7

The numbers are 7x and 7y
=> 63 and 49

Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.

[66*(5/18)] m/sec = (55/3) m/sec

Time taken to pass the man = [110*(3/55)]m/sec = 6 sec.

Let the required number of revolutions made by larger wheel be x.

Then, More cogs, Less revolutions (Indirect Proportion)

  14 : 6 :: 21 : x => 14 x x = 6 x 21

x=6*21/14  =>  x=9

In one hour, the minute hand gains 330° over the hour hand. i.e., 60 minute, the minute hand gains 330° over the hour hand.

∴ In 16 minutes, the minute hand gain over the hour hand by

Suppose the vessel initially contains 8 litres of liquid.

Let x litres of this liquid be replaced with water.
Quantity of water in new mixture =  3-3x8+xlitres.

Quantity of syrup in new mixture =  5-5x8 litres.

  3-3x8+x=5-5x8

=>   5x + 24 = 40 - 5x 

=>   10x = 16    => x = 8/5

So, part of the mixture replaced = 85×18 = 1/5.

Let the amounts to be received by P, Q and R be p, q and r.
p + q + r = 1200
p = 1/2 (q + r) => 2p = q + r

Adding 'p' both sides, 3p = p + q + r = 1200
=> p = Rs.400

q = 1/3 (p + r) => 3q = p + r

Adding 'q' both sides, 4q = p + q + r = 1200
=> q = Rs.300

r = 1200 - (p + q) => r = Rs.500.