Quantitative Aptitude - Arithmetic Ability Questions

Let Reena’s present age be 'K' yrs.
Given:{(K+3) x 4} - {(K-3) x 3)}
=> K = 21 yrs
So her present age is 21 yrs.
Then, her age after 1 year is 22 yrs.

let 't' be the time after which they met since L starts.

Given K is 50% faster than L

50 t + 1.5*50(t-1) = 300

50 t +75 t = 300 + 75

t = 375 / 125 = 3 hrs past the time that L starts

So they meet at (9 + 3)hrs = 12:00 noon.

99  = 1 x 3 x 3 x 11

101= 1 x 101

176= 1 x 2x 2 x 2 x 2 x 11

182= 1 x 2 x 7 x 13

So, divisors of 99 are 1, 3, 9, 11, 33, 99

      divisors of 101 are 1,101

      divisors of 176 are 1, 2, 4, 8, 16, 22, 44, 88, 176

      divisors of 182 are 1, 2, 7, 13, 14, 26, 91, 182

Hence , 176 hasthe most number of divisors. 

The given digits are 1, 2, 3, 5, 7, 9  

Number of even numbers = ⁵P₃ = 60.

Given,Let the cost price of single book be Rs. 100.

The cost price of (9 + 1) = 10 pair i.e. 20 books = Rs. (100 × 20) = Rs. 2000.He gets profit of 26%.

So, the selling price of 9 pair i.e. 18 books = Rs. 2000 × (126/100) = Rs. 2520

Then,the selling price of single book = Rs. 2520/18 = Rs. 140

He gives 20% discount on the marked price of a book.

That means, when the selling price is Rs. 80 then the marked price is Rs. 100.

∴When the selling price of single book is Rs. 140, the marked price = Rs. 140 × (100/80) = Rs. 175

∴The percentage increase in marked price from the cost price = (175 –100)% = 75%

Speeds of two trains = 30 kmph and 58 kmph

=> Relative speed = 58 - 30 = 28 kmph = 28 x 5/18 m/s = 70/9 m/s

Given a man takes time to cross length of faster train = 18 sec

Now, required Length of faster train = speed x time = 70/9  x  18 = 140 mts.

Given (3 Men + 4 Women + 6 Children) -----> 9 days

But W = 2M and C = M/2

Now, convert Men and Children into Women by

$$\begin{gathered} 3W2 + 4W + 6W4 \\ => 32 + 4 + 32 = 7 Women \end{gathered}$$ 

Therefore, 7 women alone can complete this work in 9 days.