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QUESTION: 1

A bag contains 25p coins, 50p coins and 1 rupee coins whose values are in the ratio of 8:4:2. The total values of coins are 840. Then find the total number of coins

Solution:

Let us assume that

Number of 25p coins = 8x

Number of 50p coins = 4x

Number of Rs. 1 coins = 2x

As per the given condition

8x + 4x + 2x = 840

14x = 840

x = 840/14

x = 60

Hence,

Amount of 25p coin = 60 × 8 × 25 = 12000 paisa = Rs. 120

Amount of 50p coin = 60 × 4 × 50 = 12000 paisa = Rs. 120

Amount of Rs. 1 coin = 60 × 2 × 1 = Rs. 120

On summing up the above-obtained values the total amount in the bag is Rs120+Rs120 +Rs 120 = Rs360

QUESTION: 2

Two vessels contains equal quantity of solution contains milk and water in the ratio of 7:2 and 4:5 respectively. Now the solutions are mixed with each other then find the ratio of milk and water in the final solution?

Solution:

Answer – A.11:7 Explanation : milk = 7/9 and water = 2/9 – in 1 vessel milk = 4/9 and water = 5/9 – in 2 vessel (7/9 + 4/9)/ (2/9 + 5/9) = 11:7

QUESTION: 3

Two alloys contain gold and silver in the ratio of 3:7 and 7:3 respectively. In what ratio these alloys must be mixed with each other so that we get a alloy of gold and silver in the ratio of 2:3?

Solution:

Answer – B.3:1 Explanation : Gold = 3/10 and silver = 7/10 – in 1 vessel gold = 7/10 and silver = 3/10 – in 2 vessel let the alloy mix in K:1, then (3k/10 + 7/10)/ (7k/10 + 3/10) = 2/3. Solve this equation , u will get K = 3

QUESTION: 4

The sum of three numbers is 123. If the ratio between first and second numbers is 2:5 and that of between second and third is 3:4, then find the difference between second and the third number.

Solution:

Answer – C.15 Explanation : a:b = 2:5 and b:c = 3:4 so a:b:c = 6:15:20 41x = 123, X = 3. And 5x = 15

QUESTION: 5

If 40 percent of a number is subtracted from the second number then the second number is reduced to its 3/5. Find the ratio between the first number and the second number.

Solution:

Answer – C.1:1 Explanation : [ b – (40/100)a] = (3/5)b.

So we get a = b.

QUESTION: 6

The ratio between the number of boys and girls in a school is 4:5. If the number of boys are increased by 30 % and the number of girls increased by 40 %, then what will the new ratio of boys and girls in the school.

Solution:

Answer – B.26/35 Explanation : boys = 4x and girls = 5x.

Required ratio = [(130/100)*4x]/ [(140/100)*5x]

QUESTION: 7

One year ago the ratio between rahul salary and rohit salary is 4:5. The ratio between their individual salary of the last year and current year is 2:3 and 3:5 respectively. If the total current salary of rahul and rohit is 4300. Then find the current salary of rahul.

Solution:

Answer – B.1800 Explanation : 4x and 5x is the last year salry of rahul and rohit respectively Rahul last year to rahul current year = 2/3 Rohit last year to rohit current year = 3/5 Current of rahul + current of rohit = 4300 (3/2)*4x + (5/3)*5x = 4300.

X = 300.

So rahul current salary = 3/2 * 4* 300 = 1800

QUESTION: 8

A sum of 12600 is to be distributed between A, B and C. For every rupee A gets, B gets 80p and for every rupee B gets, C get 90 paise. Find the amount get by C.

Solution:

Ratio of money between A and B – 100:80 and that of B and C – 100:90

so the ratio between A : B :C – 100:80:72

so 252x = 12600, x = 50. So C get = 50*72 = 3600

QUESTION: 9

The sum of the squares between three numbers is 5000. The ratio between the first and the second number is 3:4 and that of second and third number is 4:5.Find the difference between first and the third number.

Solution:

Answer – A.20 Explanation : a^2 + b^2 + c^2 = 5000 a:b:c = 3:4:5 50x^2 = 5000.

X = 10.

5x – 3x = 2*10 = 20

QUESTION: 10

The ratio between two numbers is 7:5. If 5 is subtracted from each of them, the new ratio becomes 3:5. Find the numbers.

Solution:

Answer – A.7/2, 5/2 Explanation : (7x – 5)/(5x – 5) = 3/5 X = 1/2 so the numbers are 7/2 and 5/2

QUESTION: 11

A company reduces his employee in the ratio 14 : 12 and increases their wages in the ratio 16:18, Determine whether the bill of wages increases or not and in what ratio.

Solution:

Answer – a) Decreases, 28: 27 Explanation : Let initial employee be 14a and final employee be 12a similarly initial wage is 16b and final wage be 18b Total initial wage = 14a * 16b = 224ab, total final wage = 12a* 18b = 216ab So clearly wages decreases and ratio = 224ab: 216ab = 28:27

QUESTION: 12

A bucket contains liquid A and B in the ratio 4:5. 36 litre of the mixture is taken out and filled with 36 litre of B. Now the ratio changes to 2:5. Find the quantity of liquid B initially.

Solution:

Answer – b) 56ltr Explanation : Let A = 4x and B = 5x Now, A = 4x – 36*4/9 and B = 5x – 36*5/9 + 36 Now, ratio between A and B = 2:5 X = 11.2 now B = 11.2*5 = 56

QUESTION: 13

Two numbers are in the ratio of 5:6 and if 4 is added to the first number and 4 is subtracted from the second number then the ratio becomes 3:2. Find the difference between two numbers.

Solution:

Answer – a) 2.5 Explanation : (5x + 4)/ (6x -4) = 3/2

QUESTION: 14

The income of riya and priya are in the ratio of 4:5 and their expenditure is in the ratio of 2:3. If each of them saves 2000, then find their income.

Solution:

Answer – b) 4000, 5000 Explanation : 4x – 2y = 2000 and 5x – 3y = 2000.

X = 1000, so income = 4000 and 5000

QUESTION: 15

A 50 litre of mixture contains milk and water in the ratio 2:3. How much milk must be added to the mixture so that it contains milk and water in the proportion of 3:2.

Solution:

Answer – b) 25 Explanation : (20 + x)/30 = 3/2

QUESTION: 16

Two alloys contain platinum and gold in the ratio of 1:2 and 1:3 respectively. A third alloy C is formed by mixing alloys one and alloy two in the ratio of 3:4.Find the percentage of gold in the mixture

Solution:

Answer – d) 71.3/7% Explanation : Platinum = 1/3 and 1/4 gold = 2/3 and 3/4 Alloy one and two are mixed in the ratio of 3:4, so ratio of platinum and gold in final ratio – 2:5 So gold % = (5/7)*100

QUESTION: 17

The sum of three numbers is 980. If the ratio between first and second number is 3:4 and that of second and third is 3:7. Find the difference between first and last number.

Solution:

Answer – a) 380 Explanation : ratio between three numbers – 9:12:28 49x = 980, x = 20 difference between number = 19*20 = 380

QUESTION: 18

The ratio between number of girls and boys in a school is 5: 6. If 40 percent of the boys and 20 percent of the girls are scholarship holders, what percentage of the students does not get scholarship?

Solution:

Answer – b) 69% Explanation : Girls = 5x and boys = 6x Girls that don’t get scholarship = 5x * 80/100 = 4x and boys that don’t get scholarship = 6x * 60/100 = 3.6x Percent students that didn’t get scholarship = (7.6x/11x)*100 = 69 (approx.)

QUESTION: 19

A bag contains 25p coins, 50p coins and 1 rupee coins whose values are in the ratio of 8:4:2. The total values of coins are 840. Then find the total amount in rupees.

Solution:

Answer – d) 280 Explanation : Value is given in the ratio 8:4:2. (8x/0.25) + (4x/0.5) + (2x/1) = 840.

X = 20. Total amount = 14*20 = 280

QUESTION: 20

An amount is to be divided between A, B and C in the ratio 2:3:5 respectively. If C gives 200 of his share to B the ratio among A, B and C becomes 3:5:4. What is the total sum?

Solution:

Answer – b) 6000 Explanation : s2x, 3x + 200, 5x – 200 2x/(3x + 200) = 3/5, we will get x = 600, so total amount = 10*600 = 6000

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