Question : The total number of colour blocks is 1260. If the ratio of red block to blue block is 2 : 5 and the ratio of blue block to yellow block is 15 : 7, then how many yellow blocks are there?
Option 1: 315
Option 2: 675
Option 3: 270
Option 4: 745
Correct Answer: 315
Solution :
The ratio of red block to blue block = 2 : 5 = 6 : 15
The ratio of blue block to yellow block = 15 : 7
$\therefore$ The ratio of red block to blue block to yellow block = 6 : 15 : 7
Let $6x,15x,$ and $7x$ be the numbers of red, blue and yellow blocks, respectively.
Total number of colour blocks = 1260
$⇒ 6x+ 15x+ 7x = 1260$
$⇒ 28x = 1260$
$\therefore x=\frac{1260}{28}= 45$
So, the number of yellow blocks = 45 × 7 = 315
Hence, the correct answer is 315.
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