Ratio & Proportion for Competitive Exam – Quantitative Aptitude

Ratio & Proportion (अनुपात और समानुपात) In Hindi

अनुपात (Ratio)

अनुपात दो संख्याओं या मात्राओं के बीच का संबंध है। यह बताता है कि एक मात्रा दूसरे मात्रा से कितनी गुना अधिक या कम है। अनुपात को दो संख्याओं के बीच एक कोलन (:) से अलग करके लिखा जाता है।

उदाहरण:

2:3 – यह बताता है कि पहली मात्रा दूसरी मात्रा से आधा है।
5:5 – यह बताता है कि दोनों मात्राएं बराबर हैं।

समानुपात (Proportion)

समानुपात दो अनुपातों की समानता है। इसे बराबर के चिह्न (=) से जोड़ा जाता है।

उदाहरण:

2:3 = 4:6 – यह बताता है कि पहले अनुपात में मात्राओं का संबंध दूसरे अनुपात में मात्राओं के संबंध के समान है।

Ratio & Proportion In English

Ratio:

A ratio is a comparison of two quantities of the same kind. It expresses how many times one quantity is larger or smaller than the other. It can be written in three ways:

1. a:b (a colon b)
2. a/b (a divided by b)
3. a to b (read as “a is to b”)

Example: A bag contains 4 red apples and 6 green apples. The ratio of red apples to green apples is 4:6, 4/6, or 4 to 6. This means for every 4 red apples, there are 6 green apples.

Proportion:

A proportion is an equality statement between two ratios. It states that two ratios are equivalent. Proportions are written in two ways:

1. a:b :: c:d (a is to b as c is to d)
2. a/b = c/d

The proportion can be classified into the following categories, such as:

1. Direct Proportion
2. Inverse Proportion
3. Continued Proportion

Direct Proportion

The direct proportion describes the relationship between two quantities, in which the increases in one quantity, there is an increase in the other quantity also. Similarly, if one quantity decreases, the other quantity also decreases. Hence, if “a” and “b” are two quantities, then the direction proportion is written as a∝b.

Inverse Proportion

The inverse proportion describes the relationship between two quantities in which an increase in one quantity leads to a decrease in the other quantity. Similarly, if there is a decrease in one quantity, there is an increase in the other quantity. Therefore, the inverse proportion of two quantities, say “a” and “b” is represented by a∝(1/b).

Continued Proportion

Consider two ratios to be a: b and c: d.

Then in order to find the continued proportion for the two given ratio terms, we convert the means to a single term/number. This would, in general, be the LCM of means.

For the given ratio, the LCM of b & c will be bc.

Thus, multiplying the first ratio by c and the second ratio by b, we have

First ratio- ca:bc

Second ratio- bc: bd

Thus, the continued proportion can be written in the form of ca: bc: bd