Quantitative Aptitude - Arithmetic Ability Questions

Given that, A+B = 60  and A = 2B.

Solving, We get A = 40, B = 20.

Five years their ages will be 45 and 25, so the sum of their ages will be 70.

The ratio of the ages of A and B is 3 : 5.
The ratio of the ages of B and C is 3 : 5.

B's age is the common link to both these ratio. Therefore, if we make the numerical value of the ratio of B's age in both the ratios same, then we can compare the ages of all 3 in a single ratio.

The can be done by getting the value of B in both ratios to be the LCM of 3 and 5 i.e., 15.

The first ratio between A and B will therefore be 9 : 15 and
the second ratio between B and C will be 15 : 25.

Now combining the two ratios, we get A : B : C = 9 : 15 : 25.

Let their ages be 9x, 15x and 25x.
Then, the sum of their ages will be 9x + 15x + 25x = 49x

The question states that the sum of their ages is 147.
i.e., 49x = 147 or x = 3.

Therefore, B's age = 15x = 15*3 = 45

Let Meena’s age = A.
Then Sivagami’s age = A + 2
After 6 years the total of their ages will be 7 times of what?
Not clear.
So the given data are inadequate.

Given that 

6 men and 8 boys can do a piece of work in 10 days 

26 men and 48 boys can do the same in 2 days

As the work done is equal,

10(6M + 8B) = 2(26M + 48B)

60M + 80B = 52M + 96B

=> M = 2B

=> B = M/2 ……(1)

Now Put (1) in 15M + 20B

=> 15M + 10M = 25M

Now, 6M + 8B in 10 days

=> (6M + 4M) 10 = 100M

Then D(25M) = 100M

=> D = 4 days.

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

Let B's capital be Rs. x. 

Then,3500×127x=23

=> 14x = 126000 

=> x = 9000.

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.