Question 1

If 6 men and 3 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time ?

Accepted Answer

6M + 3B = 4(1M + 1B) 6M + 3B = 4M + 4B 2M = 1B M/B = 1/2

Question 2

The sum of three numbers is 98. If the ratio of the first to the second is 2:3. And that of the second to the third is 5:8, then the second number is:

Accepted Answer

Let the three parts M, N, O. Then, M:N = 2:3 and N:O = 5:8 = (5 x 3/5) : (8 x 3/5) = 3:24/5 M:N:O = 2:3:24/5 = 10:15:24 => N = 98 x 15/49 = 30.

Question 3

80 litres of diesel is required to travel 800 km using a 800 cc engine. If the volume of diesel required to cover a distance varies directly as the capacity of the engine, then how many litres of diesel is required to travel 1000 kms using 1200 cc e…

Accepted Answer

To cover a distance of 800 kms using a 800 cc engine, the amount of diesel required = 80 litres. => the amount of diesel required to cover a distance of 1000 kms = 1000 x 80/800 = 100 litres However, the vehicle uses a 1200 cc engine and it is given that the amount of diesel required varies directly as the engine capacity. i.e., for instance, if the capacity of engine doubles, the diesel requirement will double too. Therefore, with a 1200 cc engine, quantity of diesel required = 1200/800 x 100 = 150 litres.

Question 4

The ratio of the angles of a triangle is 3 : 4 : 5. The three angles of a quadrilateral is equal to three angles of this triangle. What is the sum of the largest angle and second smallest angle of the quadrilateral ?

Accepted Answer

Angle of triangle = 180 × 3/12 = 45 deg Other angles of the triangle are = 60 deg, 75 deg Angle of quadrilateral = 360 - (45 + 60 + 75) = 180 deg Therefore, the four angles of the quadrilateral are 45, 60, 75 & 180 degrees. Hence, the sum of largest and smallest angle of the quadrilateral are 180 + 45 = 225 deg.

Question 5

In Maa Yatri Temple every devotee offers fruits to the orphans. Thus every orphan receives bananas, oranges and grapes in the ratio of 3:2:7 in terms of dozens. But the weight of a grape is 24 gm and weight of a banana and an orange are in the ratio…

Accepted Answer

Ratio of fruits (by dozen) = 3:2:7 Ratio of fruits (by weight) = 120 :150: 24 Therefore, Ratio of fruits (combined) by weight = 3 x 120 : 2 x 150 : 7 x 24 = 30 : 25 : 14

Question 6

Out of 135 applicants for a post, 60 are graduates and 80 have experience. What is the ratio of minimum to maximum number of graduates having experience?

Accepted Answer

Given total applicants = 135 Given graduates are G=60 Otherthan graduates=135-60 = 75 Given experienced candidates = 80 1) For maximum number of graduates have experience Total graduates to have experience = 60 2) For minimum number of graduates have experience Remaining after taking other than graduates in experience= 80-75 = 5

Question 7

Salaries of Karthik, Arun and Akhil were in the ratio 4 : 5 : 6 respectively. If their salaries were increased by 50 per cent, 60 per cent and 50 per cent respectively, what will be the new ratio of the salaries of Akhil, Arun and Karthik ?

Accepted Answer

Given the salaries are in the ratio of 4 : 5 : 6 Now the salaries are increased by 50%, 60% and 50% respectively The New ratio of salaries will be 4 x (150/100) : 5 x (160/100) : 6 x (150/100) = 6 : 8 : 9 The new ratio of salaries of Akhil, Arun and Karthik is 9 : 8 : 6

Question 8

In an exam, a candidate secured 504 marks out of the maximum mark of 'M'. If the maximum mark 'M' is converted into 800 marks, he would have secured 384 marks. What is the value of 'M' ?

Accepted Answer

504/M = 384/800 (504 x 800) / 384 = M M = 1050

Question 9

A mixture contains alcohol and water in the ratio 4:3. If 5 liters of water is added to the mixture, the ratio becomes 4:5. Find the quantity of alcohol in the given mixture.

Accepted Answer

Let the quantity of alcohol and water be 4x liters and 3x liters respectively. Then, (4x)/(3x+5) = 4/5 => 20x = 4(3x+5) => x = 2.5 Quantity of alcohol = (4 * 2.5) liters = 10 liters.

Question 10

A, B and C have amounts in the ratio of 3 : 4 : 5. First B gives 1/4th to A and 1/4th to C then C gives 1/6th to A. Find the final ratio of amount of A, B and C respectively.

Accepted Answer

A B C 3x 4x 5x (3x+x) 2x (5x+x) (B Gives 1/4 to A and 1/4 to C) =4x 2x 6x (4x+x) 2x 5x ( C Gives 1/6 to A) =5x 2x 5x Therefore, 5 : 2 : 5

Question 11

At a casino in mumbai, there are three tables A, B and C. The payoffs at A is 10:1, at B is 20:1 and at C is 30:1. If a man bets Rs 200 at each table and win at two of the tables, what is the maximum and minimum difference between his earnings can b…

Accepted Answer

Maximum earning will be only when he will won on the maximum yielding table. A ----> 10:1 B ----> 20:1 C ----> 30:1 i.e, he won on B and C but lost on A 20 x 200 + 30 x 200 -1 x 200 = 9800 minimum earning will be when he won on table A and B and lose on that table 3. Therefore, 10 x 200 + 20 x 200 - 1 x 200 = 6000-200 = 5800 Therefore, Difference= 9800 - 5800 = 4000

Question 12

What is the equivalent compound ratio of 5:6::7:10::6:5 ?

Accepted Answer

Given 5:6 :: 7:10 :: 6:5 We know that compound ratio is calculated as a:b :: c:d :: e:f (axcxe):(bxdxf) => (5x7x6):(6x10x5) => (210):(300) = 7:10

Question 13

The marks obtained by Vijay and Amith are in the ratio 4:5 and those obtained by Amith and Abhishek in the ratio of 3:2. The marks obtained by Vijay and Abhishek are in the ratio of ?

Accepted Answer

4:5 3:2 ------- => 12:15:10 12:10 => 6:5

Question 14

If k : l = 4 : 3 and l : m = 5 : 3, then find k : l : m ?

Accepted Answer

Given k : l = 4 : 3 l : m = 5 : 3 Then k : l : m = 20 : 15 : 9

Question 15

A company requires 12,100 strength. Present employees are 400 ladies and 6400 gents. To reach the target how many ladies required to maintain the same ratio ?

Accepted Answer

6,400 gents, 2400 ladies in that company. So total 8,800employees. for 8,800 employees, we want 2400 ladies. for 12,100employees we want how many ladies ? => (12,100/8,800) x 2400 = 3300. So we want 3300 - 2400 = 900 more ladies.

Question 16

If Rs. 782 be divided into three parts, proportional to 1/2:2/3:3/4, then the first part is:

Accepted Answer

Given ratio = 1/2:2/3:3/4 = 6:8:9 1st part = 782 x 6/23 = Rs. 204.

Question 17

A sum is divided among K, L and M in such a way that for each rupee K gets, L gets 45 paisa and M gets 30 paisa. If the share of L is Rs. 27, what is the total amount ?

Accepted Answer

K : L : M = 100 : 45 : 30 = 20 : 9 : 6 Given L share is 27 => 9 ------ 27 35 ------ ? => 105

Question 18

Pooja, Shipra and Mounika are three sisters .Pooja and Shipra are twins. The ratio of sum of the ages of Pooja and Shipra is same as that of Mounika alone. Three years earlier the ratio of age of Pooja and Mounika was 2:7 . what will be the age of S…

Accepted Answer

Since Pooja and Shipra are twins so their ages be same. Let their ages be x and age of Mounika be y , then x+x = y -------(1) and x - 3 y - 3 = 2 7 ⇒ 7 x - 2 y = 15 Now, from equation (1), 7x - 4x = 15 => x = 5 So the age of Shipra 3 years hence will be 5+3 = 8 years

Question 19

Total number of students in 3 classes of a school is 333 . The number of students in class 1 and 2 are in 3:5 ratio and 2 and 3 class are 7:11 ratio . What is the strength of class that has highest number of students ?

Accepted Answer

Ratio C1:C2 = 3:5 and C2:C3 = 7:11 So C1:C2:C3 = 21 : 35 : 55 Let the strength of three classes are 21x, 35x and 55x respectively, then Given that 21x + 35x + 55x = 333 => 111x = 333 or x=3 So strength of the class with highest number of students =55x = 55x3 = 165.

Question 20

At a game of billiards, A can give B 20 points in 60 and A can give C 15 points in 60. How many points can C give B in a game of 90 ?

Accepted Answer

a:b = 60:40 a:c = 60:45 c/a x a/b = 45/60 x 60/40 = 45/40 = 90/80 So C gives B => 10 points.

Ratio and Proportion Questions