Problems based on Ratio

A ratio is a way to compare two quantities of the same kind. It shows how many times one quantity contains another. 

Ratios are written using a colon.

The strength of a class is 50, with 30 boys and the remaining girls. Find the ratio of the number of boys to the number of girls in the class. 

Solution:

Since the strength of the class = 50

and, the number of boys in the class = 30

==> The number of girls in the class = 50 - 30 = 20 

Required ratio = `"No. of boys in the class" / "No. of girls in the class"`

                        = `30 / 20`

                        = `3 / 2`

                        = 3 : 2

A man's monthly income is ₹15,000, out of which he spends ₹12,500 every
month. Find the ratio of his

1.  savings to expenditure
2. expenditure to income
3. income to savings

Solution:

Since the monthly income of the man = ₹15,000

And his monthly expenditure = ₹12,500

His savings per month = ₹15,000 - ₹12,500 = ₹2,500 

(i) Ratio of savings to expenditure = `"₹2,500" / "₹12,500 "` = `1 / 5` = 1 : 5

(ii) Ratio of expenditure to income = `"₹12,500" / "₹15,000 "` = `5 / 6` = 5 : 6

(iii) Ratio of income to savings = `"₹15,000" / "₹2,500 "` = `6 / 1` = 6 : 1 

The ages of A and B are in the ratio 5 : 4. If B's age is 16 years, find the age of A.

Solution:
A : B = 5 : 4 => if A = 5, B is 4
                             if B = 4, A = 5. 

A's age: B's age = 5 : 4

=> if B's age = 4 years, A's age is 5 years

and, if B's age = 1 year, A's age is `5 /4` × 16 years = 20 years

Manisha bought 8 kg of rice from the market and brought it to her home. On reaching home, she found that there was a hole in the bag containing rice, because of which 800 g of rice was lost.
Find:

1.  The ratio of rice lost to the total rice bought.
2. The ratio of rice lost to the rice brought home.
3. The ratio of the rice brought home to the total rice bought

Solution:
Total rice bought = 8 kg
                            = 8000 g,
and rice lost = 800 g 
Therefore, Rice bought home = 8000 g - 800 g
                                                = 7200 g 
(i) Required ratio = `"Quantity of rice lost" / "Total quantity of rice bought "`

                             = `"800 g" / "8000 g "`

                             = `1 / 10`

                             = 1 : 10

(ii) Required ratio = `"Quantity of rice lost" / "Quantity of rice brought home"`

                              = `"800 g" / "7200 g "`

                               = `1 / 9`

                              = 1 : 9

(iii) Required ratio = `"Quantity of rice brought home" / "Total quantity of rice brought"`

                               = `"7200g" / "800 g "`

                               = `9 / 10`

                               = 9 : 10

• A ratio compares two numbers of the same unit.

• Always simplify ratios to the lowest terms.

• To share something by a ratio, add the parts, divide to find one part, then multiply for each share.

• Ratios do not have units, just numbers (like 3:2, not 3cm:2cm).