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### Mathmetics

ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

##### A fort has provisions for 250 soldiers for 35 days. After 5 days a reinforcements of 25 soldiers were arrived. Again after 10 days, 25 soldiers left the fort. How long will the remaining provisions lasting ?
 1) 12 2) 16 3) 18 4) 19 5) None of these
Explanation :
Short- Cut Methods:

ND (No. of days) = N1D1 + N2D2 = total amount of food after 5 days.
or ( 250 X 30) = ( 250 + 25) X 10 + 250 X x
or  x = 19 days .
##### The ratio of the present age of  A  to that of  B is 3 : 11.  B  is 12 years younger than C. C ''s age after 7 years will be 85 years. What is the present age of  A's  father, who is 25 years older than A ?
 1) 33 years 2) 40 years 3) 43 years 4) 48 years 5) None of these
Explanation :
Present age of C = 85 – 7 = 78 years
Present age of B = 78 – 12 = 66 years
Present age of A = 3
11 66 = 18 years
Present age of A’s father = 18 + 25 = 43 years
##### The length of a rectangle is three-fifths of the side of a square. The radius of a circle is equal to side of the square. The circumference of the circle is 132 cm. What is the area of the rectangle if the breadth of the rectangle is 8 cm ?
 1) 100.8 sq cm 2) 112.4 sq cm 3) 104.2 sq cm 4) Cannot be determined 5) None of these
##### The ratio of the adjacent angles of a parallelogram is 7 : 8. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?
 1) 136° 2) 156° 3) 168° 4) 208° 5) None of these
Explanation :
Sum of the adjacent angles of a parallelogram is 180°.
Smaller angle of the parallelogram = 7/15 × 180 = 84°
Second largest angle of the quadrilateral = 7/30 × 360 = 84°
Required sum = 84 + 84 = 168°
##### The smallest side of a right-angled triangle is 8 cm less than the side of a square of perimeter 56 cm. The second largest side of the right-angled triangle is 4 cm less than the length of the rectangle of area 96 sq cm and breadth 8 cm. What is the largest side of the right-angled triangle ?
 1) 10 cm 2) 12 cm 3) 15 cm 4) 18 cm 5) None of these
Explanation :
Side of the square = 56/4 = 14 cm
smallest side of the triangle = 14 – 8 = 6 cm
Length of the rectangle = 96/ 8 = 12 cm
Second largest side of the triangle = 112 – 4 = 8 cm
So, Largest side of the triangle =  square root of 62 + 82  = 10 cm
##### A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Chemistry part II unless Chemistry part I is also borrowed. In how many ways can he choose the three books to be borrowed?
 1) 26 2) 27 3) 41 4) 56 5) None of these
##### In how many different ways can the letters of the word ‘PREVIOUS’ be arranged in such a way that the vowels always come together?
 1) 2420 2) 2880 3) 3260 4) 4840 5) None of these
Explanation :
Treating the group of four vowels (E, I O and U) as one distinct letter then total number of letters will be 8 - 4 + 1 = 5 [i.e. P, R, V, S and (E, I, O, U)].
The five letters can be arranged in 5! = 120 ways The vowels among themselves can be arranged in 4! = 24 ways,
The letters of the word ‘PREVIOUS’ can be arranged in 120 × 24 = 2880 ways such that vowels always come together.

##### An article was sold at a profit of 15%. Had it been sold for Rs.600 more , the profit would have been 25%. At what price was it sold ?
 1) Rs.5750 2) Rs.6400 3) Rs.6090 4) Rs. 7500 5) None of these
Explanation :
Short- Cut Methods:

C.P = 600/(25-15) x 100 = 6000

So, S.P  = 6000 x 115/100 = Rs.6900
##### A milkman buys some milk. If he sells it at rupees 16 a liter, he losses 600 rupees but when he sells it at 20 a liter, he gains 600 rupees. How much milk did he purchase ?
 1) 200 litre 2) 250 litre 3) 300 litre 4) 400 litre 5) None of these
Explanation : Let, the milkman buy x liter of milk.
He sells at at rupees 16 a liter.
SP1 = Rs.16x, but losses Rs.600/
If he sells at 20 a liter, the SP2  = Rs.20x , but gains Rs.600/
Difference in SP = Rs.20x - Rs.16x = Rs.4x
Difference in actual SP = Rs.600 + Rs.600 = Rs.1200
So, 4x = 1200
or x = 1200/4 = 300