Apps 1

1) The profit earned by selling an article for Rs.832 is equal to the loss incurred when the same article is sold for Rs.448. What should be the sale price for making 50% profit?

Sol : Let C.P = Rs.x.

Then, 832 - x = x-448

=> 2x = 1280 => x=640

=> 150% of Rs.640 = Rs. 150/100 * 640 => Rs.960

Therefore, Required S.P = Rs.960

12) Salaries of Ranjani and Sudha are in the ratio 2:3. If the salary of each in increased by Rs.4000, the new ratio becomes 40:57. What is the Sudha's present salary?

Sol : Let the original salaries of Ranjani and Sudha be Rs.2x and Rs.3x respectively. Then,

= 2x+4000/3x+4000 => 40/57

=> 57(2x+4000) = 40(3x+4000)

=> 6x = 68000 =>3x=34000

Sumit's present salary = (3x+4000) = Rs. (34000 + 4000) = Rs.38000

13) Karthik started a business investing Rs.9000. After 5 months, Shyam joined with a capital of Rs.8000. If at the end of the year, they earn a profit of Rs.6970, then what will be the share of Shyam in the profit?

Sol: Karthik : Shyam = (9000 * 12) : (8000 * 7)

=> 108:56 => 27:14

=> 6970 * 14/41 = 2380

Therefore, Shyam's share = Rs.2380.

14) A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was

Sol: (A+B)'s 1 day's work = [1/45 + 1/40] = 17/360

=> Work done by B in 23 days = 1*23/40 = 23/40

=> Remaining work = 1-23/40 = 17/40

=> Now, 17/360 work was done by (A+B) in 1 day.

=> 17/40 work was done by (A+B) in 1*360/17*17/40 = 9 days.

Therefore, A left after 9 days.

15) Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is

Sol: Work done by the waste pipe in 1 minute

=> 1/15 - [1/20+1/24]

=> 1/15-11/120 = -1/40

=> volume of 1/40 part = 3 gallons.

Therefore, Volume of whole = (3*40)gallons = 120 gallons.

16) If the man walks at the rate of 5 kmph, he misses a train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station.

Sol: Let the required distance be x km.

Difference in the times taken at two speeds = 12 min = 1/5 hr.

=> x/5 - x/6 = 1/5

=> 6x-5x = 6 => x=6

Hence, the required distance is 6 km.

17) A train when moves at an average speed of 40 kmph, reaches its destination on time. When its average speed becomes 35 kmph, then it reaches its destination 15 minutes late. Find the length of the journey

Sol: Difference between timings = 15 min = 1/4 hr

Let the length of journey be x km

Then, x/35 - x/40 = 1/4

=> 8x-7x = 70

Therefore, x=70 km.

18) A train 125 m long passes a man, running at 5 kmph in the same direction in which the train is going, in 10 seconds. The speed of the train is

Sol: Speed of the train relative to man = [125/10]m/sec = [25/2]m/sec

=> [25/2 * 18/5]km/hr = 45 km/hr

Let the speed of the train be x kmph.

Then, relative speed = (x-5) kmph

Therefore, x-5 = 45 or x=50 kmph.

19) Suresh borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of 11 years is Rs.8160, how much money did he borrow?

Sol: Let the sum be Rs.x. Then,

= [x*6*3/100] + [x*9*5/100] + [x*13*3/100] = 8160

=>18x+45x+39x = (8160*100)

=> 102x = 816000

Therefore, x=8000.

20) Hari invested an amount of Rs.8000 in a fixed deposit scheme for 2 years at compound interest rate of 5 p.c.p.a. How much amount will Hari get on maturity of the fixed deposit?

Sol: = Rs.[8000*(1+5/100)2]

=> Rs.[8000*21/20*21/20]

=Rs.8820.

21) What will be the cost of gardening 1 metre broad boundary around a rectangular plot having perimeter of 340 metres at the rate of Rs.10 per square metre?

Sol : 2(l+b) = 340

Area of the boundary [(l+2)(b+2)-lb]

=> 2(l+b)+4 = 344

Therefore, Cost of gardening = Rs.(344*10) = Rs.3440

22) A cow is tethered in the middle of a field with a 14 feet long rope. If the cow grazes 100 sq.ft. per day, then approximately what time will be taken by the cow to graze the whole field?

Sol : Area of the field grazed = [22/7*14*14]sq.ft. = 616 sq.ft.

Number of days taken to graze the field = 616/100 days

=> 6 days(approx.).

23) A park square in shape has a 3 metre wide road inside it running along its sides. The area occupied by the road is 1764 square metres. What is the perimeter along the outer edge of the road?

Sol: Let the length of the outer edge be x metres. Then, length of the inner edge =(x-6)m.

=> x2-(x-6)2 = 1764

=> x2-(x2-12x+36) = 1764

=> 12x = 1800 => x=150.

Required perimeter = (4x)m = (4*150)m = 600m.

24) The diameter of the driving wheel of a bus in 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 66 kmph?

Sol: Distance to be covered in 1 min. = [66*1000/60]m = 1100m

Circumference of the wheel = [2*22/7*0.70]m = 4.4m.

Number of revolutions per min. = 1100/4.4 = 250

25) A sum of money at simple interest amounts to Rs.720 after 2 years and to Rs.1020 after a further period of 5 years. The sum is :

Sol: S.I. for 5 years = Rs.(1020-720) = Rs.300

S.I. for 2 years = Rs.(300/5)*2 = Rs.120.

Therefore, Principal = Rs.(720-120) = Rs.600.