18-01-2022 Answers

1. If (a+b):(b+c):(c+a) = 5:6:9 and a+b+c=10, what is the value of c?

Answer: 5

Solution: Let a+b=5x, then b+c=6x and c+a=9x,

Adding 2(a+b+c) = 20x,

As a+b+c=10, 20=20x and so x=1.

Now as a+b=5x=5, c=(a+b+c)-(b+c) = 10-5 = 5

2. A sum triples in 15 years at simple interest. Find the rate of interest per annum.

Answer: 13.33% per annum

Solution: Let amount be x. When tripled it is 3x.

x*15*r/100 = 2x,

r=200/15 = 13.33%

3. Mr. Manish invested Rs. 25,000 in two fixed deposits X and Y offering compound interest at 6% per annum and 8% per annum respectively. If the total amount of interest accrued in two years through both fixed deposits is Rs. 3518, the amount invested in Scheme X is

Answer: Rs.15000

Solution: Let amount A be invested in scheme X and 25000-A in scheme Y.

A*(1 + 6/100)^2 + (25000-A) * (1 + 8/100)^2 = 25000+3518,

1.1236A + (25000-A)*1.1664 = 28518

Solving A = 15000 

4. 3 men finish painting a wall in 8 days. Four boys do the same job in 7 days. In how many days will 2 men and 2 boys working together paint two such walls of the same size? 

Answer: 12 and 12/13 days

Solution: Let work to paint a wall be x.

1 men in 1 day can do x/(3*8) = x/24.

1 boy in 1 day can do x/(4*7) = x/28.

Amount of work done by 2 men and 2 boys in one day = 2*x/24 + 2*x/28

Work to be done = 2x (As two walls are to be painted).

So days required = 2x / (2x/24 + 2x/28)  = 168/13  = 12  and 12/13 days

5. A started a business investing certain amount. B joined the business after 3 months by investing same amount as A. At the end of one year received 10% of the net profit of the company as he was also managing the company operations. If in a year B received Rs.81000 as profit, what was the net profit of the company?

Answer: Rs.210000

Solution: Let the amount invested by A and B be x and the net profit be p.

Ratio of A:B investment = 12x:9x.

90% of the profit is to be shared between A and B based on their investment ratio.

B's share = 0.9p * 9x/(12x+9x) = 0.9p * 9/21 = 81000,

Net profit = 210000

6. A lab technician has one solution that is 60% chlorinated and another that is 40% chlorinated. How much litres of 40% chlorinated solution is needed to make a 100 litres solution that is 50% chlorine?

Answer: 50 litres

Solution: Quantity of 40% : Quantity of 60% = (60-50)/(50-40) = 1:1

Hence 100L will contain 50L of each solution

7. A person travels from X to Y at a speed of 40 kmph and returns by increasing his speed by 50%. What is his average speed for both the trips?

Answer: 48 kmph

Solution: Average speed = 2xy/(x+y) where x is onward journey speed and y is return journey speed.

x=40 kmph y=40*1.5 = 60 kmph

Avg speed = 2*40*60/(100) = 48 kmph

8. Two numbers are such that the square of one is 224 less than eight times the square of the other number. If the numbers are in the ratio 3:4, their sum is

Answer: 14

Solution: Let the numbers be 3a and 4a.

8*9*a^2 - 16*a^2 =  224,

Solving a=2 or -2

So their sum is 7a = 14 (which is among the given options)

9. Rs.12000 was divided among A,B,C such that A's share is Rs.2000 more than B but Rs.2000 less than C. What is B's share?

Answer: Rs.2000

Solution: Let B's share = x.

A's share = x+2000

C's share = A's share + 2000 = x+4000.

Hence x+2000 + x + x + 4000 = 12000.

x=2000

10. If   x/6 = y/96, which of the following can possibly be x+y ?

Answer: 16

Solution: If a/p = b/q = c/r , then (a+b+c)/(p+q+r).

The denominator difference is 96-6 = 90.

when x=1, the ration is 1:6. 

Hence the other fraction having ration same as 1:6 is 15:90.

So x+y = sum of numerator = 1+15 = 16.

11. In what ratio must a grocer mix two varieties of tea worth Rs.50 per kg and Rs.55 per kg so that by selling the mixture at Rs. 57.20 a kg, the gain is 10%?

Answer: 3:2

Solution: S.P. of 1 kg of the mixture = Rs. 57.20,

Gain = 10%.

So the CP = 57.20 * [100 / (100+10)]

C.P. of 1 kg of the mixture = Rs.52

So the mean price is Rs.52,

Using rule of alligation the required ratio of Rs 50 variety tea and Rs 55 variety tea =  (55-52)/(52-50) = 3:2

12. A train traveling at 100 kmph overtakes a car traveling at 64 kmph in 40 seconds. What is the length of the train in meters?

Answer: 400 metres

Solution: Relative speed = 100-64 = 36kmph = 36*5/18 = 10 m/sec

Assume the length of the caris negligible as it is not provided.

Length of train = 40*10 = 400m

13. Rs.260 was divided among A,B,C so that 12A=8B=3C. How much did B get?

Answer: Rs.60

Solution: A = 2B/3 and C=8B/3

2B/3 + B + 8B/3 = 260,

Solving B=60

14. The simple interest on a certain amount for 3 years at 14% per annum is Rs.235.20. Find the amount.

Answer: Rs.560

Solution: S.I = PNR/100,

235.20 = P*3*14/100

Required amount = P = 100 * 235.20 / (3 * 14) = 560

15. 20 men and 5 women can do a piece of work in 50 days. 5 men and 10 women can do the same work in 100 days. In how many days can the same work be done by 1 man and 1 woman?

Answer: 700 days

Solution: Let the amount of work done by a man be M and woman be W.

(20M+5W)*50 = (5M+10W)*100

1000M + 250W = 500M + 1000W,

500M = 750W,

M = 1.5W

16. Petrol and diesel are mixed in two vessels A and B in the ratio 4:3 and 2:3 respectively.  In what ratio, should Petrol and Diesel mixed in these vessels be mixed again to obtain a new mixture in Vessel C so that the mixture contains half petrol and half diesel?

Answer: 7:5

Solution: Let the quantity from vessel A be x litres and from B be y litres.

4x/7 + 2y/5 = 3x/7 + 3y/5,

x/y = 7/5

17. When X liters of fuel was added to a tank that was already one-third full, the tank was filled to 7/9 th of it's capacity. In terms of X, what is the capacity of the tank, in liters?

Answer: 9X/4

Solution: Let tank's capacity be C.

7C/9 - C/3 = X

C = 9X/4

18. A sum was invested at compound interest. The interest for the fourth year was Rs. 500 and the interest for the sixth year was Rs. 605. What was the rate of interest at which the sum was invested?

Answer: 10%

Solution: Let the interest be x%. 

Interest for fifth year = Interest for fourth year + x * interest for fourth year.  = 500 + 500* x/100 = 500 + 5x

Interest for sixth year = Interest for fifth year + x * interest for fifth year.

Hence 605 = 500+5x +  (500+5x) * x/100 

=> 500 + 5x + 5*x*x/100 + 5x  = 605 

=> 10x + x*x/20 = 105 

=> x*x + 200x - 105* 20 = 0

=> x*x + 200x - 2100 = 0

=> (x+210)(x-10) = 0 

As interest is positive x=10. Hence answer is 10%.

19. A sum invested for two years yields an interest of Rs.1200 under simple interest and Rs.1260 under compound interest. What is the sum invested?

Answer: Rs.6000

Solution: S.I for two years = 1200. Hence S.I for one year = 600.

The difference between S.I and C.I is Rs.60 which means the interes on this Rs.600 amounts to Rs.60 in one year.

Hence 600 * R = 60, R=10%.

Let the overall amount invested be A.

A * R = 600,

A * 10/100 = 600, A=6000

20. A grocer has 400 kg of coffee in stock, 20 percent of which is decaffeinated. If the grocer buys another 100 kg of coffee of which 60 percent is decaffeinated, what percent, by weight, of the grocer's stock of coffee is decaffeinated?

Answer: 28%

Solution: Total decaffeinated coffee = 20% * 400 + 60% *100 = 140 kg

Hence reqd % = 100 * 140/500 = 28%

21. 6 men can cut 12 trees in 8 days working 4 hours per day. In how many days can 12 men cut 48 trees working 8 hours a day?

Answer: 8 days

Solution: More men and more hours then less days (Indirect proportion)

More trees then more days (Direct proportion)

Days reqd * 12 * 8 * 12 = 8 * 6 * 4 * 48

Days reqd = 8

22. In a 100 m race, A beats B by 10m and C by 14m. In a race of 180m, B will beat C by

Answer: 8m

Solution: When B has travelled 90m, C would have travelled 86m.

Hence distance travelled by C when B has travelled 180m is = 180 * 86/90 = 172m.

Hence B will beat C by 180-172 = 8m

23. What is the distance between Mumbai and Goa if I took one hour more when I travel at 80 kmph than at 90 kmph?

Answer: 720 kms

Solution: Let the distance be x kms.

So x/80 - x/90 = 1

x = 720 kms.

24. Two trains move in the same direction at 50 kmph and 32 kmph respectively. A man in the slower train observes that it takes 15 seconds for the faster train to cross him. What is the length of the faster train?

Answer: 75 m

Solution: Relative speed = 50-32 = 18 kmph = 18*5/18 = 5m/sec

Length = 15*5 = 75

25. A truck starts from Bangalore to Delhi at 6am. A bus starts from Bangalore to Delhi at 8am and travels in the same path as the truck. If the speed of truck is 60kmph and that of the bus is 80kmph, at what time will the bus overtake the truck?

Answer: 2pm

Solution: Time Taken To Meet = Difference In Distance /  Relative Speed

Difference in distance = Distance travelled by truck from 6am to 8am = 2 * 60 = 120kms

Relative speed = 80 – 60 = 20 kmph

Time taken to meet (overtake) = 120/20 = 6 hrs.

Hence the bus will overtake the truck at 8am + 6hrs = 2pm.

26. Bhuvanesh starts working on a job and works on it for 10 days and completes 40% of the work. To help him complete the work, he employs Kadir and together they work for another 12 days and the work gets completed. In how many days Bhuvanesh alone can complete the work?

Answer: None of these

Solution: As Bhuvanesh completes 40% of the work done in 10 days, to complete the entire work he takes 25 days.

Let us assume Kadir can complete the entire work in y days. Let x be the entire work

Hence 0.6x = 12 days  * (x/25 + x/y )

Solving, y=100

27. Balu is five times as efficient as Dinesh and hence completes a given work in 40 days lesser time when compared to Dinesh. If both of them work together, how many days will they take to complete the work?

Answer: 8.33 days

Solution: Let Balu take x days to complete the work. As Balu is thrice as efficient, Dinesh takes 5x days.

5x-x = 40, so x=10, and 5x=50.

Let the total work be 50 units (LCM of 10 and 50).

In one day Dinesh does 50/50 = 1 unit of work and Balu does 50/10 = 5 units of work.

Together they do 6 units of work.

Num of days required by both working together = 50/6 = 8.33 days.

28. A, B and C can together do a piece of work in 20 days, A can do alone in 50 days and B in 60 days. In how many days can C do it alone?

Answer: 75 dayS

29. Three printing presses, A, B, and C, working together at their respective constant rates, can do a certain printing job in 4 hours. B and C, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take A, working alone at its constant rate, to do the same job?

Answer: 20 hours

Solution: Let total work be 20 units (LCM of 4 and 5).

Work done by A+B+C in 1 hour = 20/4 = 5 units

Work done by B+C in 1 hour = 20/5 = 4 units

Hence work done by A alone in 1 hour = 5-4 = 1 unit

So A alone will take 20/1 = 20 hours

30. Five friends jointly started a business. Three of them were sleeping partners investing certain amount. The working partner received thrice the share of the profit as received by a sleeping partner. If the net profit for a given year in the business is Rs.45000, what was the share of the profit for a working partner?

Answer: Rs.15000

Solution: Let the profit share of a sleeping partner be x.

Profit share of working partner =3x.

Hence 3*x + 2*3x = 45000, x=5000.

Profit share of a working partner = 3x = Rs.15000

31. A rabbit takes 22 leaps for every 17 leaps of cat and 22 leaps of the rabbit are equal to 17 leaps of the cat. What is the ratio of the speeds of rabbit and cat?

Answer: 1:1

Solution: Let rabbit cover a distance of r in a leap and cat cover c in a leap.

Distance covered in a given time by rabbit = 22r and by cat = 17c

Given 22r=17c which means they cover same distance in given time.

Hence the ratio of speeds is 1:1

32. A person covers a distance of 60 km in 6 hrs partly on foot at the rate of 4 km/hr and partly on a cycle at 14 km/hr. Find the distance traveled on foot.

Answer: 2.4 hours

Solution: Let time taken to travel on foot be x hrs.

4x + 14(6-x) = 60, x=2.4 hrs

33. Fifteen workers working for six hours a day can complete a work in 40 days. Then, how many days will 20 workers working for four hours a day take to complete the same work?

Answer: 45 days

Solution: Let the required number of days be x.

More workers , less days. (Indirect proportion)

More working hours , less days. (Indirect proportion)

So 15:20 :: x:40

And 6:4 :: x:40

15*6*40 = 20*4*x

x = 45 days.

34. It takes 15 seconds for a train travelling at 60 km/hour to cross entirely another train half its length and travelling in opposite direction at 48 km/hour. It also passes a bridge in 51 seconds. The length of the bridge is

Answer: 550 m

Solution: 60 kmph = 60*5/18 = 50/3 m/sec

48 kmph = 48*5/18 = 40/3 m/sec

Let the length of trains be 2L and L.

3L/(50/3 + 40/3) = 15, Solving L=150 m.

So the longer train's length = 2L = 300m

Let the length of the bridge be B.

Also it is given 2L + B = 51 * 50/3,

300+B = 850, Solving B=550 m

35. Four employees at a certain company worked on a project. The amounts of time that the four employees worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four employees worked on the project for 30 hours, which of the following cannot be the total number of hours that the four employees worked on the project?

Answer: 178

Solution: The amount of hours worked be 2x,3x,5x,6x.

If 2x=30, x=15 and the total = 16x = 240 hours

If 3x-30, x=10 and the total = 16x = 160 hours

If 5x=30, x=6 the total = 16x = 96 hours

If 6x=30, x=5 and the total = 16x = 80 hours

Hence going through the options 178 is the answer

36. Ramesh deposited Rs.5000 at x% and Rs.2000 at x+2% and Rs.1000 at x+3%, which amounted to Rs.10200 after five years at a simple interest. Had the interest being 2% more for each of the amount deposited, how much additional money would Ramesh earn as interest?

Answer: Rs.800

Solution: As it is simple interest, the value of x does not matter and hence additional money in 5 years = 2% * (5000+2000+1000) * 5 = Rs.800

37. Two farmers Hari and Krishna rented a field for grazing goats. Hari used the field for first 8 months for his 15 goats. Krishna used the field for the remaining period. If the final amount paid as rent for the year was Rs.3000 and Krishna paid Rs.600 less than Hari, how many of Krishna's goats grazed the field?

Answer: None of these

Solution: Ans: None of the above (As actual answer is 20 goats.)

Let amount paid by Hari = x, amount paid by Krishna = x-600,

x+x-600 = 3000, so Hari paid Rs.1800 and Krishna paid Rs.1200.

Let the number of Krishna's goats which grazed be x.

Hence 8 months * 15 :  4 months * x = 1800:1200 = 3:2,

x = (8*15*2)/(4*3) = 20

38. A takes 2 days to complete one-third of a job, B takes 2 days to complete one-sixth of the same work and C takes 4 days to complete half the job. If all of them work together for 2 days and C quits, how long will it take for A and B to complete the remaining work done?.

Answer: 1 day

Solution: A takes 6 days to complete the job (as 2 days for one-third), B takes 12 days to complete the job (as 2 days for one-sixth), C takes 8 days.

Let the amount of work to do the job be 24 units (24 is LCM of 6,12,8). 

In one day, A does 24/6 = 4 units, B does 24/12 = 2 units, C does 24/8 = 3 units.

So work done by A,B,C in 2 days = 2*(4+2+3) = 18 units.

Work remaining after 2 days = 24-18 = 6 units. Hence A and B will take 6/(4+2) = 1 day.

39. A can complete a piece of work in 8 hours, B can complete the same in 10 hours and C in 12 hours. A,B,C start the work together but  A leaves after 2 hours. Find the time taken by B and C to complete the remaining work?

Answer: 2 (1/11) hours

Solution: Let the total work be 120 units (LCM of 8,10,12).

In 1 hour A can do = 120/8 = 15 units , B=12 units and C=10 units.

All three start the work. In 2 hrs they complete 2*(15+12+10) = 74 units.

Now A leaves. Remaining work = 120-74 = 46 units.

B and c can do 22 units per hour.

So time taken = 46/22 = 2 (1/11) hours.

40. A sum of Rs.90 is made of 200 coins which are either 25 paise coins or 50 paise coins. The number of 25 paise coins is

Answer: 40

Solution: Average paise per coin = 9000/200 = 45

Using rule of alligation, ratio of number of 25 paise/50 paise = (50-45)/(45-25) = 5/20 = 1/4

Number of 25 paise coins = 200*1/5 = 40