## Very important Maths questions for SSC CGL-13 Series#3

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41. If a number multiplied by 25% of itself gives a number which is 200% more than the number, then the number is –

a. 12

b. 16

c. 35

d. 24

Ans : Let the number be x.

We know that x*25x/100 = x + 200x/100

=> x2/4 = 3x

=> x2 – 12x = 0

=> x – 12 = 0

We know x = 12

42. The value of an article depreciates every year at the rate of 10% of its value. If the present value of the article is Rs.729, then its worth 3 years ago was-

a. Rs.1250

b. Rs.1000

c. Rs.1125

d. Rs.1200

Ans : Let the worth 3 years ago be Rs. x.

We know that 729 = x (1 – 10/100)3

=> 729 = x*9*9*9/10*10*10

We know x = Rs. 1000

43. The price of onions has been increased by 50%. In order to keep the expenditure on onions the same the percentage of reduction in consumption has to be-

a. 50%

b. 33 1/3%

c. 33%

d. 30%

Ans : Reqd. Percentage of reduction

= 50*100/(100 + 50) %

= 5000/150 %

= 33 1/3%

44. A took two lo

Ans altogether of Rs.1200 from B and C. B claimed 14% simple interest per annum, while C claimed 15% per annum. The total interest paid by A in one year was Rs.172. Then, A borrowed-

a. Rs.800 from C

b. Rs.625 from C

c. Rs.400 from B

d. Rs.800 from B

[showhide type=“q4” ] Ans : If A borrowed Rs. x from B. and A borrowed Rs. Rs. (1200 – x) from C.

We know that (1200 – x)*15*1/100 + x*14*1/100

=> 18000 – 15x + 14x = 172*100

x = Rs. 800

45. If a regular polygon has each of its angles equal to 3/5 times of two right angles, then the number of side is-

a. 3

b. 5

c. 6

d. 8

Ans : If the number of sides a regular polygon be n.

Then (2n-4)/n = 2*3/5

=> (2n – 4)*5 = 6n

We know n = 5

46. A square is of area 200 sq. m. A new square is formed in such a way that the length of its diagonal is ?2 times of the diagonal of the given square. The the area of the new square formed is-

a. 200?2 sq.m

b. 400?2 sq.m

c. 400 sq.m

d. 800 sq.m

Ans : Length of the diagonal of Ist square

= ?2*200

= 20 m

We know Length of the diagonal of new square = 20?2m

We know Area of the new square = ½*(20.?2)2 = 400 sq. m

47. The heights of a cone, cylinder and hemisphere are equal. If their radii are in the ratio 2 : 3 : 1, then the ratio of their volumes is-

a. 2 : 9 : 2

b. 4 : 9 : 1

c. 4 : 27 : 2

d. 2 : 3 : 1

Ans : Ratio of their volumes [cone : cylinder : hemisphere]

= 1/3?(2)2h : ?(3)2*h : 2/3?(1)2.h

= 4/3 : 9 : 2/3 = 4 : 27 : 2

48. A motor-boat can travel at 10 km/hr in still water. It travelled 91 km downstream in a river and then returned to the same place, taking altogether 2 hours. Find the rate of flow of river-

a. 3 km/hr

b. 4 km/hr

c. 2 km/hr

d. 5 km/hr

Ans : Let the rate of flow of river be x km/hr.

We know that 91/(10 + x) + 91/(10 – x) = 20

=> 91(10 – x + 10 + x)(10 + x) (10 – x) = 20

=> 91*20 = 20(100 – x2)

=> x2 = 9 = (3)2

We know x = 3 km/hr

49. A man driving at 3/4th of his original speed reaches his destination 20 minutes later than the usual time. Then the usual time is-

a. 45 minutes

b. 60 minutes

c. 75 minutes

d. 120 minutes

Ans : Let the original speed be x km/hr and the usual time be y hours.

We know that x * y = ¾ x(y+1/3)

We know 4y = 3y + 1

We know y = 1 hr = 60 minutes

50. A motor-boat, travelling at the same speed, can cover 25 km upstream and 39 km downstream in 8 hours. At the same speed, it can travel 35 km upstream and 52 km downstream in 11 hours. The speed of the stream is –

a. 2 km/hr

b. 3 km/hr

c. 4 km/hr

d. 5 km/hr

Ans : Let the speeds of motor boat and the stream be x and y km/hr respectively.

We know that 39/x + y + 25/x – y = 8 …(1)

and 52/x + y + 35/x – y = 11 …(2)

Solving equations (1) and (2), we get-

We know 100 – 105/x – y = 32 – 33

We know x – y = 5

and x + y = 13

We know y = 4 km/hr

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