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Maths for competitiveMaths for competitiveexamexam

Dr. T.K. Jain.Dr. T.K. Jain.

AFTERSCHOOOLAFTERSCHOOOLM: 9414430763M: 9414430763

tkjainbkn@yahoo.co.intkjainbkn@yahoo.co.in

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By selling 45 oranges for Rs. 160 aman loses 20%, how many should hesell for Rs. 112 to gain 20% on the

whole? Selling price of 45 oranges = 160 (which is

80% of cost)

Cost of 45 oranges = 160*(100/80)=200,to earn 20%, he should have sold for 240.He has suffered a loss of Rs. 80, so firstrecover that loss. 112-80 = 32. he can sell

45 oranges in Rs. 240, so how many can hesell for Rs. 32 = 32/240(45) = 6 oranges.

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The average salary per head of allemployees of a company is Rs. 600. the

average salary of 120 officer is Rs. 4000.If the average salary per head of rest ofthe employees is Rs. 560, find the total

number of workers in the company?

Total salary of all the employees = 600x Salary of remaining persons = 560*(x-120) We already know about total salary of officers = 120*4000

= 480000 560(x-120) = 600x- 480000

560x-67200 =600x-480000 -40x = -480000 + 67200 X= 412800/40 = 10320, so other employees are 10200 Ans.

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In a lottery there are 10 prizes and 25blanks, what is the probability of

getting a prize?

10 / 35 Ans.

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There are two urns. First contains 9white, 7 red and 4 black balls. The

second contains 4 red, 5 white and 5

black balls. First we take a ball fromfirst urn and put it in the second urnand then we draw a ball from secondurn. What is the probabilty that we

draw a red ball from second urn?

Red from first box and second both: 7/20

*5/15 = 7/60 OR Other colour from first and red fromsecond: 13/20*4/15 = 13/75

Probability = 7/60+13/75 = .29 approx.

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A cone, a hemisphere and a cylinderstand on equal bases and have sameheight. What is the ratio of their

volume? Cone: pie* 1/3 *radius*radius*height

Hemisphere : 2/3 *pie*r^3

Cylinder: pie*r^2*h R is same in each case and height is

equal to radius. So the volumes are in

ratio of 1:2:3 ans.

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The ratio between the volume of asphere and volume of a circumscribing

right cylinder is? Formulae : sphere: 4/3 pie r^3 Cylinder: pie *r^2*h Let radius of sphere = 1

Volume: 4/3 pie Height of cylinder: 2 because it is double

of radius (2* radius of sphere) Volume of cylinder: 2 pie Ratio: 2:3 Ans.

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Cost of fencing a square garden is Rs.400 @ re. 1/- per meter. The area of

the garden is ? Perimeter is = 4*side

Perimeter is 400, one side = 400/4

One side of square is 100. So he area is 100*100 = 10000 sqmts.

i

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atio o t e areas o twosquares is 9:1, what is the

ratio of their perimeter? Their sides would be in ratio of 3:1

Their perimeter will also be in ratio

3:1 ans.

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e eng an rea o a rec angu arfield are 120 and 80 meters respectively.Inside the field, a park of 12 m. width ismade around the field, what is the area of

park? Area of field: 120*80 = 9600

Area of field after deducting park

(120-24)*(80-24) = 96*56 =5376 Area of park = 9600-5376=4224 Ans.

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Cost of carpeting a room 15 meter longwith a carpet 75 cm. wide at 30 paise

per meter is Rs. 36, what is breadth of

the room? Total length of carpet used : 36*(100/30)

= 120 meters

Total area of carpet = .75*120 = 90sq.meters

Formulae of area = length*breadth

Area of room is equal to area of carpet, so

breadth of room = 90/15 = 6 Ans.

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Cost of coloring four walls of a room is Rs.500. another room has length, breadth and

height just double of this room. What will be

cost of coloring in that room? Ans : 2000

Remember the formulae

2*(length+bredth)*height Now all are doubled

2*(2l+2b)*2h = so new cost will befour times.

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I buy Rs. 25 shares which gives 9%dividend but for me it is 10% return, at

what price did I buy the shares? Dividend = 9% of 25 = 2.25 This is 10 % return for me, that

means I have invested 22.5 for thisshare. Thus I purchased these shares at

22.5 (at a discount of 2.5 from facevalue).

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True discount on 1860 due after a certaiintime at 5% is 60, what is the time of the

instrument? Present value is 1800 (1860-60)

Interest rate is 5% and interest is 60

One years interest is 90, eight monthinterest is Rs. 60 so answer is 8 month.

Remember, true discount is equal tointerest on present value.

T i t i

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True iscount on a i oRs. 540 is Rs. 90, what is

bankers discount on that? Present value is 540-90 = 450, 90 on 450 is 20%,

Thus 20% interest rate has beenused. Bankers discount is interest on face

value. So 20% of 540 is 108 Ans = 108.

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Bankers gain on a sum due 2 yearshence at 5% is Rs. 8. what is the

present value? Remember, bankers gain is simple

interest on true discount.

So true discount = 8*(100/5) = 160/2(as period if 2 years) = 80

Present value = 80*(100/5) = 1600

Ans: 1600

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Bankers discont on some money is 36and true discount is 30, what is the

bill amount, bankers gain and rate? Bankers gain = 36-30 = 6

6 is 20% of 30 so rate is 20%.

Bill amount is 36*(100/20) = 180 Present value is 30*(100/20) = 150

A f R 100 d it d t

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A sum of Rs. 100 deposited atcompound interest doubles after 5

years, what will be the amount after

20 years? After 5 years twice, after 10 years,

4 times, after 15 years, 8 times and

after 20 years 16 times. Thus the amount will be 1600 ans.

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