Example 1. Solve the number riddle:
Tell me who I am! Who I am!
Take away from me the number eight,
Divide further by a dozen to come up with
A full team for a game of cricket!
Example 2. Solve the teaser:
There was in the forest an old Peepal tree
The grand tree had branches ten and three
On each branch there lived birds fourteen
Sparrows brown, crows black and parrots green!
Twice as many as the parrots were the crows
And twice as many as the crows were the sparrows!
We wonder how many birds of each kind
Aren’t you going to help us find?
Solution 1. Let the required number be x.
|The number is x.||x|
|Number eight||Means 8|
|Take away the number eight||Means −8|
|Take away from me the number eight||Means x − 8|
|Divide further by a dozen||Means (x – 8) ÷ 12|
|To come up||Means =|
|A full team for a game of cricket||Means 11 (players)|
|Final form is||(x – 8) ÷ 12 = 11|
|On transposition , ÷ changes to ×||(x – 8) = 11 × 12|
|Calculation||x – 8 = 132|
|On transposition, – changes to ×||x = 132 + 8|
|Finally||x = 140|
Therefore, required number is 140.
Solution 2. Ten and three branches means 10 + 3 = 13 branches and fourteen birds means 14 birds.
Given that, there are 13 branches and on each branch there lived 14 birds.
Total number of birds living in the tree = 13 × 14 = 182.
Three different birds are there, parrots, crows and sparrows.
Twice as many as the parrots were the crows means, the number of crows is double that of the parrots.
Twice as many as the crows were the sparrows means, the number of sparrows is double that of the crows.
Let the number of parrots be x.
|The number of parrots is x.||Number of parrots is x.|
|Number of crows is double that of the parrots||So, number of crows is 2x|
|Number of sparrows is double that of the crows||So, number of sparrows is 2 × 2x = 4x|
|Total number of birds living in the tree||= 182|
|This means||x + 2x + 4x = 182|
|Simplification||7x = 182|
|On transposition , × changes to ÷||x = 182 ÷ 7|
|Finally||x = 26|
Therefore, number of parrots = x = 26;
Number of crows = 2x = 2 × 26 = 52;
Number of parrots = 4x = 4 × 26 = 104.