CAT - Numerical Ability - 1

CAT – Numerical Ability - 1

What will come in place of question mark (?) in the following questions:-

1.        26 x 451 - ? = 6103

a)      6523               b) 5623                c) 6251                  d) 4563

Ans : (b)
? = 26 x 451 – 6103  =>  11726 – 6103 = 5623.

2.        47 x 251 - 3695 = ?
a) 8102                  b) 8100                 c) 9208                  d) 7891

Ans: (a)

3.       (12.25 x 4.02 - 14.26) x ? = 699.7
(a) 10                     b) 20                      c) 25                       d) 35

Ans: (b)
(12.25 x 4.02 - 14.26) x ? = 699.7
(49.245 - 14.26) x ? = 699.7  =>   34.985 x ? = 699.7
? = 699.70/34.985 = 20

4.       ? % of 452 = 311.88
(a) 67                     b) 52                      c)59                        d)71            e) None of these

Ans: (e)
(452 x ?)/100 = 311.88
? = (311.88 x 100)/452 = 69

5.       89% of ? + 365 = 1075.22
a)798                     b) 898                    c) 752                    d) None of these

Ans: (a)

(? x 89)/100 = 1075.22 - 365 = 710.22
? =  (710.22 x 100)/89 = 798
 

6.       A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
a) 14 years          b) 18 years          c) 20 years           d) 22 years          e) None of these

Ans: (d)
Let the son's present age be x years.
Then, man's present age = (x + 24) years. After two years the man’s age will be twice that of his on.  Thus we have an equation  (x + 24) + 2 = 2(x + 2) -->  x + 26 = 2x + 4 --> x = 22.

7.       At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present ?
a) 12 years          b) 15 years          c) 19 years           d) 21                      e) None of these

Ans: (b)
Let the present ages of Arun and Deepak be 4x years and 3x years respectively.
Then, 4x + 6 = 26 <---> 4x = 20.   x = 5. Hence, Deepak's age = 3x = 3x5 = 15 years.

8.       A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform ?
a) 120 m               b) 240 m               c) 300 m               d) data inadequate         e) None of these

Ans: (b)
Speed of the train = 54 x (5/18) m/sec = 15 m/sec.
Length of the train = the time taken to cross the man on the platform = (15 x 20)m = 300m Let the length of the platform be x metres.

Then, to cross the platform fully the train has to run its own length and the platform’s length.  The distance travelled while crossing the platform is 36 x 15 = 540 m

The length of the train + the length of the platform is 540 m. -> 300 + x = 540.

Hence the length of the platform is 540 – 300 = 240 m.

9.       A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train ?
a) 230 m               b) 240 m               c) 260 m               d) 270 m               e) None of these

Ans: (d)
Speed of the train = 72 x (5/18) m/sec = 20 m/sec.

The time taken to cross the platform of length 250 m is 26 sec.

The distance travelled in 26 sec is 26 x 20 = 520 m.

The length of the train is  520 – 250 = 270 m.  

10.   The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit ?
a) Rs. 2000           b) Rs. 2200          c) Rs. 2400           d) Data inadequate         e) None of these

Ans: (a)
Let the % of profit and % of loss which are equal be x. Then we have an equation

C.P + x = 1920   (i)         C.P – x = 1280    (ii)     where C.P. is the cost price.

Adding (i) and (ii) we have 2 C.P. = 3200 and C.P = 1600.

For getting 25% profit on this cost price of Rs 1600 the article will have to be sold at Rs 2000.