Monday, 31 August 2015

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DAILY MATHS QUIZ.

KNOWLEDGE PHILIC PRESENTS......

DAILY QUIZ.





1. A labour was employed for 40 days. He gets Rs. 10 for every working days and Rs. 2 was deducted from his wages on every leave. At the end he got total Rs. 220. Find the number of working days ?
(a)    16 days
(b)   25 days
(c)    36 days
(d)   26 days
(e)   None of these
SOLUTION. (b) 25 days
If he works for 40 days , he will get = 400
But , he got Rs 220
400 – 220 = 180.
Now, on every leave he losses Rs 10+ Rs 2 = Rs 12
So, Leave days = 180/12 = 15 days.
Working Days = 40- 15 = 25 days.

2. Rajesh was asked to calculate average of ten, two digit number. By mistakes he replaced digits of a number therefore the obtained average will decrease by 3.6. Find difference of digits of this number ?
(a)    8
(b)   3
(c)    10
(d)   4
(e)   None of these
SOLUTION. (d) 4
[(10x+y) – (10y+x)] / 10 = 3.6
9x-9y = 36
(x-y) = 4

3. Bowling rate a bowler was 15.4 per wicket. In the next match he took 5 wickets by giving 31 runs, therefore his bowling rate improved by 0.4 runs. Find number of wickets taken by him after this match ?
(a)    110 wicket
(b)   115 wickets
(c)    105 wickets
(d)   120 wickets
(e)   None of these
SOLUTION. (b) 115 wickets.
Let no. of wickets taken after this match = X
Now, acc to question,
15.4(X-5) +31 = 15X
0.4X-77+31 = 0
0.4X = 46
X=115

Also,
If we let the number of wickets before this match be X
Then, acc to question
15.4X +31 = (X+5)15
0.4X = 75-31= 44
X= 110
Hence, after this match wickets = 110+5 = 115.



4. A solution of salt and water contains 15% salt by weight. Of it 30 kg. water evaporates and the solutions now contains 20% of salt. Find the original quantity of solution ?
(a)    72 kg
(b)   80 kg
(c)    90 kg
(d)   120 kg
(e)   None of these.
SOLUTION. (d) 120 kg
Salt:Water = 15:85 = 3:17, total = 20 units
Now, after evaporating 30 kg, Ratio = 1:4
Now, since water evaporates, salt remains same
Therefore, 1:4 = 3:12
Water  evaporated = 17-12 = 5 units.
But, given water evaporated = 30 kg
Therefore, 1 unit = 6 kg
Hence, total solution = 6x(3+17) = 7x20 = 120kg.

5. 25 men can take 30 days to make 200 toys by working 6 hours/day. Find another group of 20 men can take how many days to make 400 toys by working 5 hours/day but efficiency of the first group is 3/2 times of the 2nd group ?
(a)    60 days
(b)   45 days
(c)    135 days
(d)   40 days
(e)   None of these
SOLUTION. 135 days
M1D1H1E1W2 = M2D2H2E2W1
25x30x6x1.5 x400 = 20xD2x5x1x200
D2 = 135 days.

6. A certain amount becomes triple in 5 years. This amount becomes 27 times in how many years if the interest is same ?


(a)    15 years
(b)   32.5 years
(c)    65 years
(d)   45 years
(e)   60 years
SOLUTION. (c) 65 years
Interest in 5 years = 2P
Required Interest = 26P.
2P/26P = 5/X
X= 65 years.

7. A group of 4 boys and 2 men can finish a work in 6 days, while another group of 5 boys and 6 men can finish the work in 4 days. In how many days 2 boys and 4 men will finish the work ?
(a)    5 days
(b)   12 days
(c)    6 days
(d)   2 days
(e)   None of these
SOLUTION. (e) None of these 8 (2/5) days
(4B+2M)6 = (5B+6M)4
4B = 12M
1B= 3M.
Now,
(4B+2M)6 = (2B+4M)D
4B+2M = 12M+2M = 14M and 2B+4M = 10M
14Mx6 = 10MxD
D= 84/10 = 8(2/5)days.

8. In a printing shop, 25 men can print a book of counting 200 pages in 30 days while working 6 hours per day, this book contains, 10 lines per page and each line contains 20 words. Find how many days another group of 30 men will take to print a book of 400 pages while working 5 hours per day. While this book contains 20 lines per page and each line contains 10 words. The efficiency of first group is 50% more than the second group ?
(a)    45 days
(b)   90 days
(c)    60 days
(d)   40 days
(e)   None of these
SOLUTION. (b) 90 days
25x30x6x1.5/ (200x10x20) = 30x5xDx1 / (400x20x10)
D= 5x6x2x1.5 = 90 days.

9. Tap A can empty a tank in 12 hours, while tap B can fill 5 liters water/minute in tank. If both taps open together the tank emptied in 15 hours. Find the capacity of the tank ?
(a)    20,000 litres
(b)   18,000 litres
(c)    19,000 litres
(d)   17,500 litres
(e)   None of these
SOLUTION. (b) 18,000 litres
Let the capacity be Y litres.
And Efficiency of A be X/hr
Therefore, Efficiency of B = 5/min = 300/hr
Efficiency of A+(-B) = X-300/hr.
Now, Capacity when A works alone = 12hrs* X/hr = 12X = Y
Capacity When Aand B worked together = 15hrs*(X-300)/hr = 15(X-300)= Y
But, Capacity is same. Therefore,
12X= 15(X-300) = Y
3X= 4500
X= 1500
Y = 12X= 12*1500 = 18,000 litres.

10. When price of milk increased by 25% by what percentage a household should reduce consumption of the milk, so that total expenditure increased by only 10% ?
(a)    15%
(b)   16%
(c)    18%
(d)   12%
(e)   None of these
SOLUTION (d) Expenditure = Price*Consumption
New price = 1.25 of Original Price
New Expenditure = 1.10 of Original Expenditure.
New Consumption = ?
1.10Exp = 1.25Price*Consumption
110/125= 0.88 = New Consumption
So reduction = 1-0.88 = .12= 12%

11. A person sells his table at profit of 25% and chair at a loss of 20%. But, on the whole he gains Rs. 18. On the other hand, if he sells the table at 20% loss and chair at 25% gain, he neither gains nor losses. Find the Cost Price of Table and Chair.
(a)    200,160
(b)   160,200
(c)    250,180
(d)   210,170
(e)   None of these
SOLUTION(a) 200,160
Let CP of Table and Chair be X and Y respectively.
1.25X + 0.80Y = X+Y+18
25X-20Y = 1800.… (i)
Also,
0.80X+1.25Y = X+Y
25Y = 20X
Y = 4X/5…(ii)
Putting (ii) in (i), we get
25X-20x4X/5= 1800
9X = 1800
X= 200
Y= 160




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