Mathmetics

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

Q21.
The simple interest per annum on  an amount of Rs.17,000 at the end of four years is Rs.6800. What would be the compound interest on the same amount at the same rate after 2 years ? 
1) Rs.3240 2) Rs.3470
3) Rs.3570 4) Can'not be determined
5)None of these
Answer : Rs.3570
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Q22.
The ratio between A's and Bs salary was 3:4,two year ago . The ratio's of individual salaries of A and B two year's ago and this year's salaries are 4:5 and 2:3 respectively. At present the total of their salary is Rs.4290. What is present salary of A ?
1) Rs.1560 2) Rs.1600
3) Rs.1650 4) Rs.1840
5)None of these
Answer : Rs.1650
Explanation :
Let, two year ago ,the ratio of between A'and B's salary was 3x: 4x respectively.

The ratio of their individual salary between two years ago and this year is 4y:5y and  2z:3z respectively.
So, 4y = 3x (A's last year salary)
or y = .75x   and  2z = 4x (B's last year salary)
 or z = 2x
Now, the total of their salary is Rs.4290 . 
So, 5y + 3z = Rs.4290
Replace y with .75x; replace z with 2x
So, 5(.75x) + 3(2x) = 4290
or 3.75x + 6x = Rs.4290    or 9.75x = 4290
or x = 4290/9.75 = 440
Then, A's present salary 3.75 (440) = Rs.1650

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Q23.
Alok takes 8 more days than Bikas to finish a work. Alok and Bikas start the work and Bikas leaves the task 9 days before the work is finished. If Alok completes 75% of the overall work, how long would Alok have taken to finish the work if he had worked independently? 
1) 8 days 2) 10 days
3) 12 days 4) 14 days
5)None of these
Answer : 14 days
Explanation : Let, Bikas takes x days to finish the work . So, Alok would take (x +8) days to finish the same work.
Given, Alok finishes 75% and Bikas finishes 25% work respectively. 
So, (x+8)3/4 = (x/4)+9
or (3x+24)/4 = (x+36)/4
or 2x = 12
or x = 6

Therefore, Alok would finishes the work (6+8) = 14 days alone.

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Q24.
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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Q25.
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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Q26.
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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Q27.
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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Q28.
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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Q29.
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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Q30.
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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