Mathmetics

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

Q61.
A river is flowing at 2 kmph. It takes a man twice as long to row up as, to row down the river. What is the rate (in km/hr) of the man in still water ?
1) 2 2) 4
3) 6 4) 8
5)None of these
Answer : 6
Explanation :
Let,speed of boat man be x kmph.
So, speed in down stream =(x+2) kmph. and speed in up-stream = (x-2) kmph.
Since, distance is constant for both case ,
the equation = 2(x-2) = (x+2)
or 2x-4 = x+2
or x= 6 kmph

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Q62.
The speed of a car increases by 2 km after every hour. If the distance travelled in the first hour was 35 km. What was the total distance travelled in 12 hours ?
1) 456 km 2) 482 km
3) 548 km 4) 552 km
5)None of these
Answer : 552 km
Explanation :
Given, the first term,  a = 35, common difference, d = 2 and total number of terms,  (n) = 12. 
The sum of this series will be the total distance travelled.
Sum,  Sn= n/2[2a + (n - 1) d] = 6 [70 + 11 x 2] = 552 km.

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Q63.
A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:
1) 3 2) 5
3) 9 4) 11
5)None of these
Answer : 11
Explanation :
Let, the ten's digit be x and unit's digit be y.
Then, number = 10x + y.
Number obtained by interchanging the digits = 10y + x.
(10x + y) + (10y + x) = 11(x + y), which is divisible by 11.
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Q64.
The cost of 16 pens and 12 pencils is Rs. 720. What is the cost of 20 pens and 15 pencils ?
1) Rs.800 2) Rs.840
3) Rs. 880 4) Rs.900
5)None of these
Answer : Rs.900
Explanation :
Let, the price of the pen be ‘x’ and that of a pencil be ‘y’.
16x + 12y = 720 or (16x) X 5/4 + 12y X 5/4 = 720 X 5/4 
or 20x + 15y = 900
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Q65.
The ratio of the sum and the difference of two numbers is 3: 1. Then what is the ratio of these two numbers ?
1) 3 : 2 2) 2 : 1
3) 3 : 1 4) 4 : 3
5)None of these
Answer : 2 : 1
Explanation :
Let, the number be ‘x’ and ‘y’
So, (x+y)/(x-y) = 3/1
or x + y = 3x - 3y  
or 2x = 4y
or x:y = 2:1 
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Q66.
The sum of two numbers is 28 and their difference is 4. What is the product of the two numbers ?
1) 184 2) 192
3) 196 4) 212
5)None of these
Answer : 192
Explanation :
(x + y)2 = (x - y)2  + 4xy
or x + y = 28, x - y = 4
or 4xy = (28)2 - (4)2
or 4xy = (28 + 4) (28 - 4)
or xy =  = 32 x 6 = 192
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Q67.
A,B and C have to distribute Rs.1200 among themselves. A and C together have Rs. 700 and B and C have Rs.800. How much amount does C have ?
1) Rs.400 2) Rs.500
3) Rs.600 4) Rs.300
5)None of these
Answer : Rs.300
Explanation :
Given, A + B + C = 1200
or A + B + 2C = 700 + 800 = 1500
or 1200 - C + 2C = 1500
or C = 1500 - 1200 = 300
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Q68.
A man spends 1/3rd of his salary on food  and 2/5th on house rent. Then he saves an amount of Rs. 2000 per month. What is his monthly salary ?
1) Rs.6500 2) Rs. 7500
3) Rs.9000 4) Rs.12000
5)None of these
Answer : Rs. 7500
Explanation : Let, the man's income be Rs.x.
Expenditure on food = x/3 and expenditure on house rent = 2x/5
His saving = x - (x/3 + 2x/5) = 4x/15
So,4x/15 = 2000
or x =( 2000 X 15 ) /4 = 7500.
 
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Q69.
The ratio between the present ages of A and B is 2 : 3 respectively. Four years ago, the ratio between their ages was 5 : 8. respectively. What will be A’s age after 7 years ?
1) 29 yrs 2) 35 yrs
3) 31 yrs 4) 33 yrs
5)None of these
Answer : 31 yrs
Explanation :
Let, the present ages of A and B be 2x years and 3x years respectively.
So, (2x-4)/(3x-4) = 5/8
or 16x - 32 = 15x -20 
or  x = 12
Therefore, the Ages of A after 7 years = 2x + 7 = 2 x 12 + 7 = 31 years

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Q70.
Three men or eight boys can do a piece of work in 17 days. How many days will two men and six boys together take to finish the same work ?
1) 9 days 2) 11 days
3) 14 days 4) 12 days
5)None of these
Answer : 12 days
Explanation :
3 men = 8 boys
2 m = (8/3)x2 =  16/3 boys.
(2 men + 6 boys) = (16/2)+6 boys =  34/3boys
8 boys can complete the work in 17 days
or 34/3boys boys can complete the work in x days
or (34/3) : 8 = 17 : x
or x =(17x8x3)/34  = 12 days
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