22-10-2021 Answers

1. The average age of 3 girls is 20 years and their ages are in the proportion 3:5:7. The age of the youngest girl is

Answer: 12 years

Solution: Sum of ages = 3*20 = 60.

Let the ages be 3x,5x,7x,

Adding, 15x=60, x=4.

Hence youngest girl's age = 3x = 12 years

2. The numerator and the denominator of a fraction are in the ratio 3 : 4. When both are increased by the same value, the ratio becomes 4 : 5. Which of the following could be the value added?

Answer: All of these

Solution: Let the numerator be 3x. Then the denominator is 4x. If y be the quantity

added, then

(3x + y)/(4x + y) = 4/5

(15x + 5y) = (16x + 4y)

x = y.

So for every value of x there is a value of y.

3. Monthly earnings of two persons are in the ratio 4:5 and their monthly expenses are in the ratio 7:9. If each saves Rs.5000 per month, their respective monthly incomes are

Answer: Rs. 40000 and Rs.50000

Solution: Let the monthly incomes be Rs.4x and Rs.5x respectively and monthly expenses be Rs.7y and Rs.9y respectively.

So 4x-7y = 5x-9y = 5000

From the above equations,

y = x/2.

4x - 7x/2 = 5000, x = 10000

4x = 40000 and 5x = 50000.

4. If a:b=3:7, find the value of (5a+b):(4a+5b)

Answer: 22:47

Solution: a/b = 3/7, So 7a=3b, a=3b/7.

Substituting this in (5a+b):(4a+5b), we get 

 15b/7 + b : 12b/7 + 5b, 

After cancelling common factors the ration is= 22:47

5. Find x:y:z, if 2x+y-5z = 0 and 3x-2y-4z=0

Answer: 2:1:1

Solution: Multiply eq1 with 2 and add it with eq2.

We get 7x-14z=0,  x=2z.

Substitute this in eq1,

4z+y-5z=0, y=z.

Hence the ration x:y:z = 2z:z:z = 2:1:1

6. Two containers of equal volume are fully filled with a mixture of alcohol and water in the ratio 3:5 and 5:7 respectively. If the content of both the containers are poured into a third container, what would be the ratio of alcohol to water in the third container?

Answer: 19/29

Solution: Alcohol:Water in container-1 = 3x:5x

Alcohol:Water in container-2 = 5y:7y.

But as volumes are equal, 8x = 12y,  x=1.5y

Combined ratio of alcohol : water = (3x+5y) : (5x + 7y) = 19/29

7. Three sons P, Q, R of a land lord sold their land for Rs.64 lakhs and then decided to divide the amount among them in the ratio 3:2:1. They paid 4 lakhs as sales tax. Find the amount obtained by Q finally.

Answer: Rs.20 lakhs

Solution: Amount remaining after sales tax = 64-4 = 60 lakhs.

The dividing amount be 3x,2x,x.

60 lakhs = 3x+2x+x, solving x=10lakhs.

Q's amount = 2x = 20 lakhs.

8. The income of a husband and wife are in the ratio 3:2 and their expenses are in the ratio 5:3. If each save Rs.2000, what is the income of the husband?

Answer: Rs.12000

Solution: Let income be 3x and 2x. Expense be 5y and 3y.

3x-5y = 2000; 2x-3y = 2000

So, x=2y.

Solving y=2000 and x=4000.

Husband's salary = 3x = 12000

9. During a given week A programmer spends 1/4 of his time preparing flow chart, 3/8 of his time coding and the rest of the time in debugging the programs. If he works 48 hours during the week, how many hours did he spend debugging the program?

Answer: 18 hrs

Solution: Proportion spent in debugging = 1 - 1/4 -3/8 = 3/4 - 3/8 = 3/8th

So debugging time = 48*3/8 = 18 hrs

10. If a quarter kilogram of tomato costs 60 paise, how many paise will 200 grams cost?

Answer: 48 paise

Solution: Cost of 200 gms of tomato = (60*200)/250 = 48 paise.

11. A certain shade of Grey paint is obtained by mixing 3 parts of white with 5 parts of black paint. If 2 gallons of mixture is needed and the individual colours can be purchased only in one gallon or half gallon cans, what is the least amount of paints in gallons that must be purchased in order to measure out the portions needed for mixture?

Answer: 2.5 gallons

Solution: Ratio of white paint = 3/8 and black = 5/8.

As 2 gallons of mixture is needed,

Amount of white paint needed = 2*3/8 = 6/8 = 0.75 gallons. As paint can be bought in one or half gallon cans, 1 gallon of white paint should be bought to get 0.75 gallons.

Amount of black paint needed = 2*5/8 = 5/4 = 1.25 gallons. Here again as paint can be bought in one or half gallon cans, 1.5 gallon of black paint should be bought to get 1.25 gallons.

So least amount of gallons to be purchased = 1+1.5 = 2.5 gallons.

12. In a class of 80, 4/5 th own car and 15/16 of them own ALTO. How many own ALTO?

Answer: 60

Solution: Number of people who own car = 80*4/5 = 64.

People owning ALTO = 64*15/16 = 60.

13. The cost of making a toy car is divided into cost of material, cost of repair and cost of painting in the ratio of 5:2:3. The cost for material is Rs.200. Find the total cost in making the car?

Answer: 400

Solution: Let the cost of material,repair and painting be 5x,2x and 3x.

5x=200, Hence x=Rs.40.

So total cost = 5x+2x+3x = 10x = Rs.400.

14. A wealthy lady has 3 sons A,B,C. She decides to share her entire property such that her sons get the share in the following ratio - A/B = 3:5, B/C=5:7. If son A got 60 crores worth property as his share, how much did son C get?

Answer: 140 crores

Solution: A/B = 3/5        B/C = 5/7

Shortcut:

The ratio of A:B:C is given as (n1*n2) : (d1*n2) : (d1*d2).

Hence A:B:C = (3*5):(5*5):(5*7) = 15:25:35

Now 15x=60, x= 4 crores.

Hence amount D got = 35x = 140 crores.

15. A man owns 2/3 rd of a market research business and sells 3/4 th of his shares for Rs. 75000. What is the value of the business?

Answer: Rs. 150000

Solution: Let the total number of shares be x.

2x/3 * 3/4 gives 75000

so, for x shares it is = 75000*4/2 =75000*2 = 1,50,000 Rs

16. A bag contains 440 coins. There are only 25p, 50p and Re.1 coins. The total amount in the bag is Rs.320. If the ratio of number of 25p coins to Re.1 coin is 1:3, find the number of 50p coins.

Answer: 120

Solution: Let the number of 25p coins be 4x.

Num of Re.1 coin = 12x.

Let num of 50p coins be 2y.

4x+12x+2y = 440 - Eqn 1

4x/4 + 12x + 2y/2 = 320 - Eqn 2

Solving eqn 1 and 2,

x=20, y=60.

Number of 50p coins = 2y = 2*60 = 120

17. Three buses travel from Bangalore to Salem and the average speed of the buses are in the ratio 2:3:5. What is the ratio of the time taken by the buses to travel?

Answer: 15:10:6

Solution: Let the total distance be 30 units (LCM of 2,3,5).

Time taken by car1 = 30/2=15, car2 = 30/3=10, car3=30/5=6.

Hence time taken ratio = 15:10:6

18. If the ratio of the sum and the difference of two numbers is 25:1, what is the ratio of the two numbers?

Answer: 13:12

Solution: Let the numbers are x and y respectively.

(x+y)/(x-y) = 25:1

25x-25y = x+y; 24x = 26y

x/y = 26/24 = 13:12

Hence the required ratio is 13:12.

19. A fox takes 5 leaps for every 4 leaps of a tiger, but 3 leaps of a tiger covers the distance covered by 4 leaps of fox. What is the ratio of the speed of tiger to that of the fox?

Answer: 16: 15

Solution: Let the distance covered by a fox in one leap = x and tiger be y.

3y = 4x, y=4x/3.

In a given period of time, fox takes 5 leaps covering 5x.

Tiger takes 4 leaps = 4y = 4*4x/3.

Ratio of speed = 16x/3 : 5x = 16:15

20. A bottle is filled with 3 parts of water and 5 parts of milk. What percentage of this mixture must be drawn off and replaced with water so that 50% water is present in the mixture?

Answer: None of these

Solution: Current amount of water = 3x and milk = 5x. Combined amount=8x.

Let the amount of mixture to be withdrawn and replaced with water be y.

So,  3x - y * 3x/8x + y = 5x - y * 5x/8x,

3x - 3xy/8x + y = 5x - 5xy/8x,

3x - 3y/8 + y = 5x -5y/8,

2x = y + 2y/8,

2x = 5y/4, y = 8x/5.

As total quantity is 8x, one-fifth or 20% of the mixture should be drawn off and replaced with water.

21. The ratio of the incomes of A and B are in the ratio 1 : 2 and the ratio of their expenses in 1 : 5. Who is saving more?

Answer: Cannot be determined

Solution: Let incomes be x,2x

Expense = y,5y

Savings ratio = x-y : 2x-5y = x-y : x-y + (x-4y)

As both x and y are positive, x-4y can be negative or positive. Hence we cannot determine with the given data.

22. A car travels 12 kms with a 4/5th filled tank. How far will the car travel with 1/3 filled tank?

Answer: 5 kms12 kms for 4/5th tank.

For 1/3rd tank it is = (12 * 1/3) / 4/5 

= 12 * 1/3 * 5/4 = 5kms.

23. If the ratio of the sum and the difference of two numbers is 8 : 3, what is the ratio of the two numbers?

Answer: 11:5

Solution: Let the numbers be x and y respectively.

(x+y)/(x-y) = 8/3

8x-8y = 3x+3y

5x = 11y

x/y = 11/5

Hence the required ratio is 11:5.

24. What numbers should be added to each one of 6, 14, 18 and 38 to make them equally proportionate ?

Answer: 2

Solution: (6 + x) / (14 + x) = (18 + x) / (38 + x)

Solving, x = 2

25. A debtor can pay 70 paisa in the rupee, but if his creditors would take 40% of his debts, he could pay them and have Rs.50 left. The value of his debts is

Answer: Rs.500

Solution: Let his debts be x.

Assets = 0.70x

Also 0.6x + 50 = 0.7x,

x=50/0.10 = 500