Ratio and Proportions problems and solutions
What is a ratio?
A ratio is a representation of distribution of a value present among the persons present and is shown as follows:
If a total is divided among A, B and C such that A got 4 parts, B got 5 parts and C got 6 parts then it is represented in ratio as A:B:C = 4:5:6.
So, 4:5:6 means that the total value is divided into 4+5+6 = 15 equal parts and then distributed as per the ratio.
Divide Rs. 580 between A and B in the ratio of 14:15.
A:B = 14:15 => 580 is divided into 29 equal parts => each part = Rs. 20.
So A’s share = 14 parts = 14 x 20 = Rs. 280
B’s share = 15 parts = Rs. 300.
If A:B = 2:3 and B:C = 4:5 then find A:B:C.
To combine two ratios the proportions common for them shall be in equal parts. Here the common proportion is B for the given ratios.
Making B equal in both ratios they become 8:12 and 12:15 => A:B:C = 8:12:15.
Three numbers are in the ratio of 3: 4 : 8 and the sum of these numbers is 975. Find the three numbers.
Let the numbers be 3x, 4x and 8x. Then their sum = 3x+4x+8x = 15x = 975 => x = 65.
So the numbers are 3x = 195, 4x = 260 and 8x = 520.
Two numbers are in the ratio of 4 : 5. If the difference between these numbers is 24, then find the numbers.
Let the numbers be 4x and 5x. Their difference = 5x – 4x = x = 24 (given).
So the numbers are 4x = 96 and 5x = 120.
Given two numbers are in the ratio of 3 : 4. If 8 is added to each of them, their ratio is changed to 5 : 6. Find two numbers.
Let the numbers be a and b.
A:B = 3:4 => A / B = 3 / 4.
Also, (A+8) / (B+8) = 5 / 6.
Solving we get, A=12 and B = 16
A garrison has provisions for 120 soldiers for 240 days. After 180 days 60 more soldiers will join the group. For how many more days will the provisions last?
Actually after 180 days,
If 120 members are there provisions come for 60 more days (since total 240 days)
But now 180 members are there.
So number of days = (120/180) X 60 = 40 days.
If 24 men working for 12 hrs a day can do a work in 16 days, in how many days can 8 men working 6 hrs a day do it?
24 men – 12 hrs – 16 days
8 men – 6 hrs – ? days (n)
n =16 X (12 / 6) X (24 / 8) ( since no of hrs reduced no of days has to increase and no of men reduced also increases no of days i.e., inverse proportional)
=> n = 96 days.