Maths 20 May 2

Maths for competitive exam Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk

www.afterschoool.tk

By selling 45 oranges for Rs. 160 a man loses 20%, how many should he sell 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 first recover that loss. 112-80 = 32. he can sell 45 oranges in Rs. 240, so how many can he sell for Rs. 32 = 32/240(45) = 6 oranges. www.afterschoool.tk

The average salary per head of all employees of a company is Rs. 600. the average salary of 120 officer is Rs. 4000. If the average salary per head of rest of the 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.

www.afterschoool.tk

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

• 10 / 35 Ans.

www.afterschoool.tk

There are two urns. First contains 9 white, 7 red and 4 black balls. The second contains 4 red, 5 white and 5 black balls. First we take a ball from first urn and put it in the second urn and then we draw a ball from second urn. 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 from second: 13/20*4/15 = 13/75 • Probability = 7/60+13/75 = .29 approx. www.afterschoool.tk

A cone, a hemisphere and a cylinder stand on equal bases and have same height. 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.

www.afterschoool.tk

The ratio between the volume of a sphere 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.

www.afterschoool.tk

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.

www.afterschoool.tk

Ratio of the areas of two squares 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.

www.afterschoool.tk

The length and breadth of a rectangular field are 120 and 80 meters respectively. Inside the field, a park of 12 m. width is made 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.

www.afterschoool.tk

Cost of carpeting a room 15 meter long with 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 = 90 sq.meters • Formulae of area = length*breadth • Area of room is equal to area of carpet, so breadth of room = 90/15 = 6 Ans.

www.afterschoool.tk

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 be four times.

www.afterschoool.tk

An investor owning 1000, Rs. 5 share in a compay, sells 400 of them. He invests the proceeds in a stock at 90. calculate the total income in 1 year from shares. He gets 6.5% in first and 7.25% in second shares as dividend? • Investor still has 600 shares valuing 3000 as face value – on which he gets 6.5% = return = 195/• He sells the 400 shares and gets 2000. • He invested Rs. 2000 in other shares – which he got in Rs. 90 (face value must be 100) = 2000*100/90 = 2222(face value). • His return is 7.25% on face value=166. • Total return = 195+166 = 361 ans. • Assumption – we have assumed that the face value of the second share is Rs. 100.

www.afterschoool.tk

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 this share. • Thus I purchased these shares at 22.5 (at a discount of 2.5 from face value).

www.afterschoool.tk

True discount on 1860 due after a certaiin time 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 year’s interest is 90, eight month interest is Rs. 60 so answer is 8 month. • Remember, true discount is equal to interest on present value.

www.afterschoool.tk

True discount on a bill of Rs. 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 been used. • Banker’s discount is interest on face value. So 20% of 540 is 108 • Ans = 108. www.afterschoool.tk

Banker’s gain on a sum due 2 years hence at 5% is Rs. 8. what is the present value?

• Remember, banker’s 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

www.afterschoool.tk

Bankers discont on some money is 36 and true discount is 30, what is the bill amount, banker’s gain and rate?

• • • •

Banker’s 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

www.afterschoool.tk

A sum of Rs. 100 deposited at compound 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.

www.afterschoool.tk

www.afterschoool.tk

Thanks Afterschoool conducts three year integrated PGPSE (after class 12 along with CA & CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.

www.afterschoool.tk

www.afterschoool.tk social entrepreneurship for better society

www.afterschoool.tk