13-09-2021 Answers

1. If Rs.24586 is to be divided among four persons A,B,C,D such that A:B = 3:4, B:C = 5:6 and C:D = 7:5, who will get the minimum amount?

Answer: Person A

Solution: A/B = 3/4     B/C = 5/6   C/D=7/5

Shortcut:

The ratio of A:B:C:D is given as (n1*n2*n3) : (d1*n2*n3) : (d1*d2*n3) : (d1*d2*d3).

Hence A:B:C:D = (3*5*7):(4*5*7):(4*6*7):(4*6*5) = 105:140:168:120

Hence A will get minimum amount.

2. Three cans contain equal quantities of alcohol and water in the ratios  6:1, 5:2 and 8:3 respectively. If the contents of all three cans are poured into a single vessel, the proportion of alcohol:water in the vessel is

Answer: 59:18

Solution: Let the quantity of alcohol and water be 6x:x , 5y:2y and 8z:3z.

Proportion of alcohol:water = (6x+5y+8z)/(x+2y+3z). --Eq1

As all the cans contain equal quantities of alcohol and water, 7x = 7y = 11z.

Hence x=y and z=7y/11.

Substituting in Eq1), the required proportion is

(6y + 5y + 56y/11)/(y + 2y + 21y/11) = 177y/54y = 59:18

3. A,B,C,D are employees working in a manufacturing company and they work to produce 54, 71, 75 and 99 units respectively. A newly appointed manager wanted to make the ratio of units produced by A:B to be equal to the ratio of units produced by C:D by subtracting same number of units from the work of all four A,B,C,D. What is the number of units to be reduced?

Answer: 3 units

Solution: Let the additional unit to be produced be x.

(5+x)/(9+x) = (11+x)/(22+x),

The shortcut is given by the formula x = (ad-bc)/((a+d)-(b+c))

As  a=54, b=71, c=75, d=99

x= (5346 - 5325)/(153-146) = 21/7 = 3

4. Tom, Dick and Harry went for lunch to a multi-cuisine restaurant. Tom had $100 with him, Dick had $60 and Harry had $40. Tom preferred continental, while Harry chose Chinese. Dick opted for mughlai cuisine. Continental and Chinese types of items tasted good than that of mughlai. Despite, variations in ordering, they called for a single bill. They got a bill for $104 and decided to give a tip of $16. They further decided to share the total expenses in the ratio of the amounts of money each carried. The amount of money which Tom paid more than what Harry paid is

Answer: 36$

Solution: Total bill = 120 $.

Total money the three carried = 100+60+40 = 200$

Let money paid by Harry for the bill = 120 * 40/200 = 24$,  Tom = 120* 100/200 = 60 $. Difference = 60-24 = 36$.

5. If a:(b+c) = 1:3 and c:(a+b) = 5:7, find b:(a+c).

Answer: 1/2

Solution: (b+c)/a = 3/1, Hence (a+b+c)/a = 4/1 = 12/3

(a+b)/c = 7/5, Hence (a+b+c)/c = 12/5 

Thus a:c:(a+b+c) = 3:5:12.

Thus b = 12 - (3+5) =4.

So, b/(a+c) = 4/8 = 1/2

6. A merchant buys 20 kg of wheat at Rs.30 per kg and 40 kg wheat at Rs.25 per kg. He mixed them and sells one third of the mixture at Rs.26 per kg. The price at which the merchant should sell the remaining mixture, so that he may earn a profit of 25% in his whole transaction is

Answer: Rs.37 per kg

Solution: Cost Price = 20*30 + 40*25 = Rs.1600

After mixing he gets a mixture of 60kgs. In this he sells 20kgs at Rs.26 per kg. So he has got 20 * 26 = Rs.520. 

To get a overall 25% profit, he should sell the mixture for Rs.1600 * 1.25 = Rs.2000.

So he should sell the remaining 40kg mixture at (Rs.2000 - Rs.520)/40 = Rs.37 per kg.

7. A worker was to be paid Rs. 200 and a shirt for 12 days of work. But due to his illness he left after working for 9 days and was paid Rs. 120 and a shirt. What is the price of the shirt?

Answer: 120 Rs

Solution: Based on the ratio and proportion, he has worked for 3/4 th of the expected time.

Hence the worker should receive 3/4 * 200 + 3/4 th of shirt which is 150 rs and 0.75th of shirt

 But as he received a shirt and 120rs, the difference of 150-120 = 30 rs is towards the additional 0.25th of shirt.

Hence price of shirt = 4 * 30 = 120 Rs.

8. From each of two given numbers, half the smaller number is subtracted. Of the resulting numbers the larger one is three times as larger as the smaller. What is the ratio of the two numbers?

Answer: 2:1

Solution: Let the number be x and y, y being smaller.

x-y/2 : y-y/2 = 3:1. So x:y = 2:1

9. A milkman mixes 2 litres of water with 8 litres of milk. After selling 25% of the mixture, he adds water to replenish the quantity sold. What is the current proportion of milk to water?

Answer: 3:2

Solution: Initial quantity = 10 litres out of which 25% = 2.5 litres was sold.

Now remaining quantity = 7.5 litres of which 7.5/5 = 1.5 litres is water and remaining 6 litres is milk.

Now he added 2.5 litres of water. So now the mixture has 1.5+2.5 = 4 litres of water and 6 litres of milk.

Required proportion of milk:water = 6:4 = 3:2.

10. The annual income of Babu and David is in the ratio 6:5. Their expense in that year is in the ratio 4:3. If both of them save Rs.3000 at the end of the year, what is the income of Babu?

Answer: Rs. 9000

Solution: Let the income of Babu and  David be  6x and 5x.  

Income - Savings = Expense. Hence,

(6x-3000)/(5x-3000)  = 4/3,

18x - 9000 = 20x - 12000,

Solving x= 1500,

Babu's income = 6x = Rs.9000

11. Three cans contain equal quantities of alcohol and water in the ratios  6:1, 5:2 and 10:3 respectively. If the contents of all three cans are poured into a single vessel, the proportion of alcohol:water in the vessel is

Answer: 71/20

Solution: Let the quantity of alcohol and water be 6x:x , 5y:2y and 10z:3z.

Combined proportion of alcohol:water = (6x+5y+10z)/(x+2y+3z). --Eq1

As all the cans contain equal quantities of alcohol and water, 7x = 7y = 13z.

Hence x=y and z=7y/13.

Substituting in Eq1), the required proportion is

(6y + 5y + 70y/13)/(y + 2y + 21y/13)

= 213y/60y = 71/20

12. The ratio of income of A and B is 3:4. The ratio of their expenditure is 4:5. Find the ratio of their savings, if the savings of A is one fourth of his income?

Answer: 12:19

Solution: Income of A = x, B = 4x/3

Savings of A = one fourth of his income = x/4.

Expense of A = Income - Savings = x - x/4 = 3x/4. Expense of B = 5 * 3x/4 * 1/4. 

Savings of B = Income - expense = 4x/3  - 15x/16 = 19x/48 = x/4 : 19x/48 = 12:19

13. A and B are two alloys of gold and copper prepared by mixing metals in the ratio 7: 2 and 7: 11 respectively. If equal quantities of these alloys are melted to form a third alloy C, the ratio of gold and copper in C will be

Answer: 7:5

Solution: Let x units of alloys be considered.

Gold in alloy C = 7x/9 + 7x/18 = 21x/18

Copper in alloy C = 2x/9 + 11x/18 = 15x/18. Ration = 21:15 = 7:5

14. The ratio of boys to girls in a school is 20:11. If 50 more girls were needed to make this ratio 5:4, what was the number of boys in the school?

Answer: 200

Solution: Let the number of boys and girls to begin with be 20x and 11x.

20x/(11x+50) = 5/4, solving x=10.

Num of boys = 20x = 20*10 = 200.

15. The total income of A,B,C is Rs.5400. If after spending 80%, 50% and 75% of their income respectively, the ratio of their savings is 4:9:4. What is the income of C?

Answer: Rs.1600

Solution: Let the savings of A,B,C be  4x,9x,4x.

Their income will be  20x, 18x, 16x.

Now 5400 = 20x+18x+16x, solving x=100.

Income of C = 16x = Rs.1600

16. If x:y = 2:3, find the value of (3x+4y):(4x-y).

Answer: 18/5

Solution: Assume x=2 and y=3 as in their ratio.

Required value = 18/5

17. A milkman supplies 200 litres of milk to 100 houses in a colony on a daily basis. One day after supplying milk to 20 houses, he spilt certain amount of milk by accident. So he added 5 litres of water to compensate the loss. After adding water the quantity remaining in the milk can was thrice the quantity of the milk he had supplied already. What was the quantity of milk that was supplied to the initial 20 houses?

Answer: 50 litres

Solution: Let milk supplied to houses before milk is spilt = x litres.

Amount left is thrice he had supplied already which is 3*x = 3x.

Hence 200 = 3x+x = 4x. x=50 litres.

Amount supplied to the initial 20 houses = x = 50 litres.

18. For every 200 rupees spent by the research department, sales department spends 20 Rs. For every 400 Rs spent by the sales department, the advertising department spends 150 Rs. The triple ratio of the money spent by the research department to the money spent by the sales department to the money spent by the advertising department can be expressed as

Answer: 80:8:3

Solution: The common department is sales department.

Research:Sales = 200:20  and Sales:Advertisement = 400:150.

Dividing by common factors,

Research:Sales = 10:1  and Sales:Advertisement = 8:3

Multiplying Research:Sales by 8, Research:Sales = 80:8  and Sales:Advertisement = 8:3.

Now the ratio is 80:8:3

19. Magesh spends 30% of his income on petrol. 1/4th of the remaining on house rent and the balance on food. If he spends Rs.300 on petrol then what is the expenditure on food?

Answer: Rs.525

Solution: Let income be x. Petrol expense = 0.3x,  House rent = 1/4 * 0.7x, food expense = 3/4 * 0.7x

As petrol expense = 300 = 0.3x, x=1000.

Hence food expense= 3/4 * 0.7 * 1000 = Rs.525

20. Rs. 9605 is to be divided among A,B,C in such a way that after deducting Rs.28. Rs.32 and Rs.45 from their respective shares, the remaining money with A,B,C is in the ratio 6:4:9. Find B's share.

Answer: Rs.2032

Solution: Let the ratio of money they finally have ve 6x,4x,9x.

Then 19x + 105 = 9605, Solving x = 500.

Money finally with B=4x = 2000.

B's share = 2000+32 = 2032

21. (A lady become very rich by writing children comic books and she has 4 sons A,B,C,D. She decides to share her entire property such that her sons get the share in the following ratio - A/B = 3:5, B/C=2:3 and C/D=5:3. If son A got 240 crores worth property as his share, how much did son D get?

Answer: 360 crores

Solution: A/B = 3/5    B/C = 2/3   C/D = 5/3

Shortcut:

The ratio of A:B:C:D is given as (n1*n2*n3) : (d1*n2*n3) : (d1*d2*n3) : (d1*d2*d3).

Hence A:B:C:D = (3*2*5):(5*2*5):(5*3*5):(5*3*3) = 30:50:75:45

Now 30x=240, x=8 crores. So, amount D got = 45x = 360 crores.

22. Three married couples attended a new year party. For all the three couples the ratio of husband and wife's age was 7/6. The sum of the ages of the husbands was 105. If the sum of the ages of two of the wives was 60, what was the age of the third wife?

Answer: 30 years

Solution: Let the ages of husbands be h1,h2,h3 and wives be w1,w2,w3.

As h1/w1 = h2/w2 = h3/w3 = 7/6,

then (h1+h2+h3)/(w1+w2+w3)  = 7/6.
105/(60+w3) = 7/6, Solving w3 = 90 - 60 = 30

23. 7/8 of 3/7 of a number is equal to 25% of 45% of another number.  What is the ratio of the first and the second numbers respectively?

Answer: 3:10

Solution: First number be x and second number be y.

7/8 * 3/7  * x = 3x/8.

0.25 * 0.45 * y = 0.45y/4

Now 3x/8 = 0.45y/4, x/y = 0.9/3 = 3/10.

24. An orange colored glass has Orange juice and white colored glass has Apple juice both of equal volumes. 50ml of the orange juice is taken and poured into the white glass. After that similarly, 50ml from the white glass is poured into the orange glass. Of the two quantities, the amount of apple juice in the orange glass and the amount of orange juice in the white glass, which one is greater and by how much?

Answer: Both are equal

Solution: Assume there is  x ml in each glass.

When 50 ml of orange juice is poured into white glass, ratio of apple : orange =  x : 50

Now 50ml of the mixture is poured into orange glass.

Now orange glass contains:

x-50 ml + 50 *50/(x+50) of orange and  50 * x/(x+50) of apple juice.

Now white glass contains:

50 - 50 * 50/(x+50) of orange juice and x - 50 * x/(x+50) of apple 

Now ratio of apple : orange = 50 * x/(x+50) : 50 - 50 * 50/(x+50)

= 50x/(x+50) : (50x + 2500 -2500)/(x+50)

= 50x/(x+50) : 50x/(x+50) = 1:1

25. If Rs. 1564 be divided into three parts, proportional to  1/2 : 2/3 : 3/4, then the second part is

Answer: None of these

Solution: LCM of denominators is 12.

Multiplying by 12, the ratio becomes, 6:8:9.

Hence second part = 1564 * 8/(6+8+9) = Rs.544