Mathmetics

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

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Q1.
A rectangular container, whose base is square of side 15cm,stands on a horizontal table and holds water up to 3cm from the top. When a cube is  placed in the water and is completely submerged, the water rises to the top and 54cm^3 of water overflows. What is its surface area?
1) 448cm2 2) 464cm2
3) 486cm2 4) 524cm2
5)None of these
Answer : 486cm2
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Q2.
The length of a rectangle increases by 20% and also  its breadth increases by 15% . What should be the percentage change in its perimeter?
1) 35% 2) 36%
3) 38% 4) Can't be determined
5)None of these
Answer : Can't be determined
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Q3.
A is 25% more efficient than B and 50% more efficient than  C. A and B together can complete a work in 20 days. How many days the same work  can be completed by B and C if both work  in alternate days and B starts  the work  first  ?
1) 48 days 2) 49 days
3) 50 days 4) 51 days
5)None of these
Answer : 49 days
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Q4.
A person invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B ?
1) Rs.6400 2) Rs.6500
3) Rs.7200 4) Rs.7500
5)None of these
Answer : Rs.6400
Explanation :
Explanation:
Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x).
Then, (x x 14 x 2)/100 + ((13900 - x) x 11 x 2) /100= 3508
28x - 22x = 350800 - (13900 x 22)
or 6x = 45000
or x = 7500.
So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.
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Q5.
Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

What will be the compound interest earned on an amount of Rs. 5000 in 2 years ?

I. The simple interest on the same amount at the same rate of interest in 5 years is Rs.2000.      
II. The compound interest and the simple interest earned in one year is the same.
III. The amount become more than double on compound interest in 10 years.

1) I only 2) I and II only
3) II and III only 4) I and III only
5)None of these
Answer : I only
Explanation :
Explanation:
P = Rs. 5000 & T = 2 years.
I. S.I. on Rs. 5000 in 5 years is Rs. 2000.
    (5000 x R x 5)/100  = 2000   or       R = 8.
Thus I only gives the answer.
Correct answer is (1).
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Q6.
Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

       What is the area of the hall ?
I. Material cost of flooring per square meter is Rs. 2.50
II. Labour cost of flooring the hall is Rs. 3500
III. Total cost of flooring the hall is Rs. 14,500.
1) I and II only 2) II and III only
3) All I, II and III 4) Any two of the three
5)None of these
Answer : All I, II and III
Explanation :
Explanation:
   I. Material cost = Rs. 2.50 per m2
 II. Labour cost = Rs. 3500.
III. Total cost = Rs. 14,500.
Let the area be A sq. metres.
Material cost = Rs. (14500 - 3500) = Rs. 11,000.
5A/2 = 11000  or    A = (11000 x 2 )/5 = 4400 m2.
Thus, all I, II and III are needed to get the answer.
Correct answer is (3).
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Q7.
A person invested some amount at the rate of 12% simple interest and a certain amount at the rate of 10% simple interest. He received yearly interest of Rs. 130. But if he had interchanged the amounts invested, he would have received Rs.4 more as interest. How much did he invest at 12% simple interest ?
1) Rs.400 2) Rs.500
3) Rs.700 4) Rs.800
5)None of these
Answer : Rs.700
Explanation :
Explanation :
Let the amount invested at 12% be x and the amount invested at 10% be y respectively

x x 12 x 1)/100 +( y x 10 x 1)/100 = 130
1.2x + y = 1300
Similarly, 1.2y + x = 1340
or (1.2x) x 1.2 + 1.2y = 1300 x 1.2
x +1.2y = 1340
     or 0.44x = 1560 - 1340 = 220
    or x = (220/0.44) - Rs. 500  
    or y = 1300 - 1.2 x 500 = Rs. 700

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Q8.
A person invested some amount at the rate of 12% simple interest and a certain amount at the rate of 10% simple interest. He received yearly interest of Rs. 130. But if he had interchanged the amounts invested, he would have received Rs.4 more as interest. How much did he invest at 12% simple interest ?
1) Rs.400 2) Rs.500
3) Rs.700 4) Rs.800
5)None of these
Answer : Rs.700
Explanation :
Explanation :
Let the amount invested at 12% be x and the amount invested at 10% be y respectively

x x 12 x 1)/100 +( y x 10 x 1)/100 = 130
1.2x + y = 1300
Similarly, 1.2y + x = 1340
or (1.2x) x 1.2 + 1.2y = 1300 x 1.2
x +1.2y = 1340
     or 0.44x = 1560 - 1340 = 220
    or x = (220/0.44) - Rs. 500  
    or y = 1300 - 1.2 x 500 = Rs. 700

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Q9.
A cylindrical container of height 14 m and base diameter 12 m contains oil. This oil is to be transferred to one cylindrical can, one conical can and a spherical can. The base radius of all the containers is same. The height of the conical can is 6 m. While pouring some oil is dropped and hence only 3/4th of cylindrical can could be filled. How much oil is dropped ?
1) 36 pie m3 2) 48 pie m3
3) 50 pie m3 4) 54 pie m3
5)None of these
Answer : 36 pie m3
Explanation :
Explanations:
Volume of the oil =  22/7x 62 x 14 = 504 x 22/7 m3.
Base radius of all the containers = 7 m
Volume of the spherical can = (4/3) x (22/7)x 63 m3.
Volume of the conical can =  (1/3) x (22/7) x 62 x 6 m3 = 72 x (22/7)
Balance oil = Volume of the cylindrical can 
= 504 (22/7) - 288 (22/7)- 72(22/7) = 144(22/7) m3.
Oil dropped = 1/4 th of the cylindrical can
= 1/4x 144 = 36 (22/7) m3.
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Q10.
A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface area of the remainder is 8/9th of the curved surface of the whole cone, what should be the ratio of the line segments into which the cone’s altitude is divided by the plane is given by ?
1) 2 : 3 2) 1 : 3
3) 1 : 2 4) 1 : 4
5)None of these
Answer : 1 : 2
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