Page 15 - CITS - WCS - Mechanical

WORKSHOP CALCULATION - CITS

EXERCISE 2 : Ratio & Proportion

A ratio is an ordered set of two numbers a & b, written a/b where b does not equal 0.A proportion is an equation
in which two ratios are set equal to each other. For example, if there is 1 girl and 3 boys you could write the ratio
as: 1 : 3 (for every one girl there are 3 boys) 1 / 4 are girls and 3 / 4 are boys
A proportion is a type of ratio that connects with a part to a whole. For example, in the class with 20 women & 80
men, the total class size is 100, and the proportion of women is 20/100 or 20%. The proportion of men is 80/100
or 80%.
Trade related problems
Q 1. If a: b = 3: 7 and b: c = 8: 5, then find a: b: c.
Solution
Here, we make the common term ‘b’ equal in both ratios.
Therefore, we multiply the first ratio by 8 and the second ratio by 7.
So, we have a : b = 24 : 56 and b : c = 56 : 35
Thus, a : b : c = 24 : 56 : 35
Q 2. Find the mean proportional between 0.23 and 0.24.
Solution

We know that the mean proportional between ‘a’ and ‘b’ is the square root of (a x b).
=> Required mean proportional = \sqrt(0.23 \times 0.24) = 0.234946802
Q 3. Divide Rs. 672 in the ratio 5: 3
Solution
The given ratio is 5 :3
Sum of numbers in the ratio = 5 + 3 = 8
We divide Rs. 672 into 8 parts.
672 / 8 = 84
Therefore, Rs. 672 in the ratio 5: 3 = Rs. 672 in the ratio (5 / 8) : (3 / 8)
=> Rs. 672 in the ratio 5 :3 = (5 x 84) : (3 x 84) = 420 : 252
Q 4. A bag contains 50 p, 25 p, and 10 p coins in the ratio 2: 5 : 3, amounting to Rs. 510. Find the number of coins
of each type.
Solution
Let the common ratio be 100k.
Number of 50 p coins = 200 k
Number of 25 p coins = 500 k
Number of 10 p coins = 300 k
Value of 50 p coins = 0.5 x 200 k = 100 k
Value of 25 p coins = 0.25 x 500 k = 125 k
Value of 10 p coins = 0.1 x 300 k = 30 k
=> Total value of all coins = 100 k + 125 k + 30 k = 255 k = 510 (given)
=> k = 2
Therefore, Number of 50 p coins = 200 k = 400
Number of 25 p coins = 500 k = 1000
Number of 10 p coins = 300 k = 600

Q 5. A mixture contains sugar solution and colored water in the ratio of 4 : 3. If 5 liters of colored water is added
to the mixture, the ratio becomes 6 : 7. Find the initial quantity of sugar solution in the given mixture.

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