CSC - Aptitude

CSC - Aptitude

1.       One year ago, the ratio of Roonie’s and Ronaldo’s age was 6: 7 respectively. Four years hence, this ratio would become 7: 8. How old is Ronaldo ?

                Ans-36 years

                Let the ages of Roonie and Ronaldo one year ago be X and Y.

One year ago the ratio of their ages was   X : Y ::  6 : 7  This will give you the value of Y as 7X/6   ----------- (a)

After four years from now the ratio of the ages will become  (X+5) :  (Y+5)  ::  7 : 8

è 8X + 40 = 7Y + 35 -> 7Y = 8X + 5  Substituting the value of Y from (a)

We have 7 x 7X/6 = 8X + 5 -> 49X = 48X + 30 -> X = 30 and Y = 35.

Ronaldo’s present age is Y+1 -> 35 + 1 = 36 years.

2.       In what ratio must rice at Rs. 9.30 per kg be mixed with rice at Rs. 10.80 per kg so that the mixture be worth Rs. 10 per kg ?

Ans-8:7

                                                                                9.30                                        10.80

                         

                                                                                                                      10.00              

                                                                                0.80                                        0.70

Using the Rule of Alligation we find the ratio as 8 : 7.

               

3.       One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field.

Ans-120m²

Using Pythagoras theorem we find the length of the other side as 8 m and hence the area is

15 x 8 = 120 sq.m

4.       A rectangular grassy plot 110 m. by 65 m has a gravel path 2.5 m wide all round it on the inside. Find the cost of gravelling the path at 80 paise per sq. meter

Ans- Rs 680

The overall area of the grassy plot is 110 x  65 -> 7150 sq. meters.

The gravel path is 2.5 m wide all around. This would reduce the dimensions of the remaining grassy plot by 5 m on all sides.

Hence the area of the grassy plot after applying the gravel path is  105 x 60 -> 6300 sq. meters.

Hence, the area of the gravel path is  7150 – 6300 = 850 sq.mtrs.  The cost of gravelling the path at the rate of 0.80 paise per sq.mtr  will be 850 x 0.80 ->  Rs 680.00

5.       There are two sections A and B of a class consisting of 36 and 44 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class?

Ans-37.25 kg

The total weight of Section A   ->       40 x 36 ->  1440 kg

The total weight of Section B   ->       35 x 44 ->   1540 kg.

Total weight of both sections (80 students)  ->   2980 kg

Hence the average weight of whole class ->    2980 / 80 = 37.25 kgs

6.       The milk and water in two vessels A and B are in the ratio 4 : 3 and 2: 3 respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel C containing half milk and half water?

Ans-7 : 5

This is a tricky question. In vessel A milk is 4 parts out of total 7 parts.

In vessel B milk is 2 parts out of total 5 parts. Hence, the temptation to answer the question will be 1 : 1

The question is in what ratio the liquids in both the vessels are to be mixed. If the liquids are mixed in the ratio of the total parts in the two vessels then the vessel C into which these are poured will have half milk and half water.

Hence the answer is ->  7 : 5.

7.       Of the three numbers, second is twice the first and is also thrice the third. If the average of the three numbers is 44.Find the largest number.

Ans-72

Let the first number be ‘x’. Then the second number is ‘2x’ and the third number be ‘y’.

Since the average of the three numbers is 44 the total of the three numbers is 132.

Hence we have the equation  x + 2x + y = 132. We are informed the second number is thrice the third number.   Hence, we have 2x = 3y or y = 2x/3. Substituting this value of Y

We have a new equation  x + 2x + 2x/3 = 132.Solving we get the value of ‘x’ as 36.

Applying this value, we get the three numbers as  36, 72 and 24.

Hence the largest number is 72.

8.       Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are black or both are queen?

Ans-55/221

Probability (Black or Queen) =  P(Black ) + P(Queen) – P(Black, Queen)

è 26C2 + 4C2 – 2C2 -> 660/2652 ->  55/221

9.       A bag contains 6 white and 4 black balls. 2 balls are drawn at random. Find the probability that they are of same color.

Ans-7/15

                (6C2 + 4C2)/10C2

10.   A, Band C are three contestants in a km race. If A can give B a start of 40 m   and A can give C a start of 64m how many meters’  start can B give C ?

Ans:  25 meters.

When A covers 1000 meters, B covers 960 meters and C covers 936 meters.

Thus when B runs 960 meters C can run only 936 meters.

In other words in a race of 960 meters B can give C a start of 24 meters.

Thus in a race of 1000 meters ( One Km) B can give C a start of

(24 * 1000)/ 960 -> 25 meters.