Mathmetics

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

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Q1.
A person sold two hens for Rs. 105 each . On one he lost 25% . On the other he gained 50% . What is the gain or loss on his total outlay ?
1) 12.5% 2) 20%
3) 28.3% 4) Neither gain Nor loss
5)None of these
Answer : Neither gain Nor loss
Explanation : Short-Cut Method:

[100 x (Profit - Loss ) x 2 x Profit x Loss] / (100 + Profit ) + (100 - Loss) = 0%
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Q2.
A sells his books cost Rs.500 to B at a profit of 30%. After some period of time, B sells the same book to A at a loss of 20%. What is the total % of profit or loss in the whole trading ?
1) 4% profit 2) 4% loss
3) 26% profit 4) 26% loss
5)None of these
Answer : 26% profit
Explanation : Let, CP of A = 100 ,  SP of B from A = 130 i.e. profit = 30/
Again , some days B sells in return to A at loss of 20% i.e. the CP of A again = 130 x (80/100) = 104

So ,in the whole trade , he gets actual profit =  (30-4) = 26  i.e. 26% 
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Q3.
Two partners invested Rs.20,000 and Rs.12,000 respectively in a business.They distribute 75% of the profit equally and distribute the rest  25% according to the ratio of their investment of capitals. If  the bigger partner received Rs.400 more than the other, then what is the total profit ?
1) Rs.5280 2) Rs.5600
3) Rs.6240 4) Rs.6400
5)None of these
Answer : Rs.6400
Explanation : Since, 75% of the profit is distributed equally ,rest 25% should be distributed according to their ratio of investment.
Actual, ratio of capital = 20000:12000 = 5:3
5/8 - 3/8 = 400
or 2/8 = 1/4 = 400 
or 1 = 4 x 400 = 1600 i.e. 25% 
So, total profit = 400 x 4 x (1/25) x 100 = 6400

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Q4.
The L.C.M and H.C.F of two numbers are 660 and 10 respectively. If the sum of the numbers is 170, what is the difference between the numbers ?
1) 50 2) 56
3) 60 4) 64
5)None of these
Answer : 50
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Q5.
A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes ?
1) 1 : 6 2) 1 : 5
3) 1 : 25 4) 1 : 125
5)None of these
Answer : 1 : 5
Explanation :
The volume of the larger cube = 53 = 125 cm3.
The volume of each of the smaller cubes = 13 = 1 cm3
         Therefore, one would get 125 smaller cubes.
The surface area of the larger cube = 6a2 = 6(52) = 6  25 = 150
The surface area of each of the smaller cubes = 6 (12) = 6.
Therefore, surface area of all of the 125, 1 cm3 cubes = 125  6 = 750.
Therefore, the required ratio = 150 : 750 = 1 : 5
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Q6.
1) 8 2) 9
3) 10 4) 12
5)None of these
Answer : 10
Explanation :
Given, x2 + 9/x = 6x
Or x2 - 6x = 9
Or (x-3)2 = 0  
Or x = 3
So, x2 + 9/x= 10
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Q7.
If  a = 4/3, then, what is the value of 27a3 -108a+ 144a - 317  ?
1) 221 2) -231
3) -253 4) 0
5)None of these
Answer : -253
Explanation :
Given, a = 4/3
Or  3a = 4 
Or 3a - 4 = 0
Or (3a-4)3 = 27a3 - 108a2 + 144a - 64 = 03
Or 27a3 - 108a2 + 144a - 317 = (27a3 - 108a2 + 144a -64) - 153 = 0 - 253 = - 253
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Q8.
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
Answer : 19
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 .
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Q9.
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
Answer : 43 years
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
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Q10.
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
Answer : 100.8 sq cm
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