Polaris - Aptitude - 1

Polaris – Aptitude - 1

1.       I have marbles in three different colours as follows:
Blue 60;  Green 156;  Red 204
I distribute them to children in such a way that each one of them get equal number of marbles and all in one colour.
How many children are there?
(a) 12                     (b) 35                    (c) 67                     (d) 31
Ans: (b)

Find the HCF of 60, 156 and 204. The HCF is 12. Total number of marbles is 420. Divide this by the HCF -> 420/12 = 35.

2.       A square of side 6cm has a circle inscribed in it. Calculate the approximate ratio of surface area of the circle to square.
(a) 11/14              (b) 13/14              (c) 12/14              (d) 14/18
Ans: (d)

The area of the Square is 6*6 = 36 sq.cm.  The radius of the circle if half the side of the square – 3 cm. The area of the circle is πr² -> 22/7 * 3 * 3 = 28 sq.cm (approx.)

Hence the ratio is 28 : 36 or 14 : 18

3.       There are 3 numbers whose ratio is as follows: first: second=2:3 and second : third= 5:8. There sum is 98, what is the second number?
(a) 20                     (b) 30                    (c) 40                     (d) 50
Ans: (b)

Let the three numbers be A, B and C. We now have two ratios

A : B :: 2 : 3  …….. (i)     and  B : C :: 5 : 8 ……….. (ii)

We have two different values for B in the two ratios. Let us make this common in both the ratios.

Multiply (i) by 5 and (ii) by 3.

We now have one common ratio ->    A : B : C :: 10 : 15 : 24

The sum of A + B + C = 98.  Hence the value of B is ->  98 * 15/49 = 30.

4.       A 30% saline solution is to be converted to a 10% saline solution. How much pure water needs to be added to 100 kg of 30% saline solution?
(a) 150 kg             (b) 100 kg            (c) 200 kg             (d) 250 kg
Ans: (c)

In 100 kg saline solution the salt is 30 kg. This quantum of salt will remain as such in the 10% saline solution also. Since the quantum of salt is 30 kg and its percentage is 10% only the total quantum of solution should be 300 kg.

Hence 200 kg of water needs to be added.

5.       In a given factory, average salary combined for the staff and supervisors is Rs 60 while that for only staff is Rs. 56. The average salary of supervisors is Rs. 400. There are a total of 12 supervisors. How many labourers are employed in this factory?
(a) 1020                (b) 1130                (c) 1500                (d) 1532
Ans: (a)

This question can best be answered through Rule of Alligation figure as under.

                          A (56)                                                          B (400)
                                  

                                                                X (60)           

                       B – X (340)                                                 X – A (4)

From the above we observe the ratio of staff and supervisors as 340 : 4

We are informed that there are 12 supervisors.

3 Parts of supervisors amount to 12.

Hence the number of staff is 340 * 3 = 1020.

6.       Alok completed a journey from his home to mall in 42 minutes at an average speed of 10kmph. He walked initially at 4kmph and then took an auto which moved at 25kmph. What part of his journey did he walk?
(a) 1km                 (b) 2km                                (c) 3km                 (d) 4km
Ans: (b)
The distance covered in 42 minutes t an average speed of 10 kmph is -> 10 * 42/60 = 7 km.

Let ‘x’ be the distance travelled by walking at a speed of 4 kmph. Then 7-x is the distance travelled by auto at a speed of 25 kmph.  We now have an equation:

x/4 + (7-x)/25 = 42/60. Solving we get the value of x as 2 km.

Hence, the distance covered by walking is 2km.

7.       Ashish can do 1/4 of his work in 10 days, Vijay 40% in 40 days and Deepak 1/3 in 13 days. Who finishes first?
(a) Ashish            (b) Deepak         (c) Vijay                                (d) Can’t say
Ans: (b)

Ashish ……. In 10 days does ¼th work. So, to complete the whole work will take 40 days.

Vijay in 40 days will complete 40% or 2/5 of the work. He will take 100 days to complete the work.

Deepak in 13 days completes 1/3^rd of the work and would take 39 days to complete the whole work.

Hence, Deepak will complete the work first.

8.       You can complete a carpet weaving in 10 days while I can do it in 15 days. We work together but I leave in 2 days. How many days will you now require to finish the work?
(a) 7                       (b) 8                       (c) 19/3                 (d) 20/3
Ans: (d)

In one day I will do 1/10 work and my friend will do 1/15 work. Together we both in one day will do 1/10 + 1/15 = 5/30 -> 1/6 work. In two day we both will do 1/6 * 2 = 1/3 work.

The remaining work now is 1 – 1/3 = 2/3 which I alone will have to do.

The time taken by me to complete this work is ----- (2/3) / 1/10 = 20/3 days.

9.       Increase in population for a given country in three consecutive years is 10%, 25% and 10%. What is the combined percentage increase for the three years?
(a) 45%                 (b) 52%                 (c) 51.25%           (d) 45.25%

Ans: (c)

Successive percentage increase for two years is given by the formula -> x + y + xy/100 where x and y are the percentage variation of two successive periods.

Applying this, we get the percentage variation at the end of 2^nd year as -> 10 + 25 + 250/100 = 37.50%

Now the variance between the second and third year is ->  37.50 + 10 + (37.50*10)/100

= 51.25% 

10.   Sheila and Sunita start a business with investment of Rs8000 and Rs5000 resp. Sunita is an active partner and so she gets 10% of profit separately for supervision. If the total profit is Rs 3240/-, then what is the share of profit for Sunita?
(a) 1445                (b) 1334                (c) 1500                (d) 324
Ans: (a)

Ratio of Shiela and Sunita’s investment are :  8 : 5

10% of total profit of Rs 3240/- is Rs 324/- and this Sunita gets separately.

Remaining profit is --- 3240 – 324 = 2916.

Sunita’s share in this profit is ->     2916 * 5/13 =1121.

Hence, Sunita’s share of profit in the business is ----  1121 + 324 = 1445.