State whether the following statement is true or false
$400 c m : 2 m : : 450 c m : 3 k m$

True

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False

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Solution

The correct option is B False
Step-1: Convert $2 m$ and $3 k m$ in $c m$
$2 m$ $= 2 \times 100 =$ $200 c m$ ( As $1 m = 100 c m$ )
$3 k m$ $= 3 \times 1, 00, 000 =$ $3, 00, 000 k m$ ( As $1 k m = 1, 00, 000 c m$ )
Now, $400 c m : 2 m : : 450 c m : 3 k m$ equivalent to $400 c m : 200 c m : : 450 c m : 3, 00, 000 c m$
Step-2: write $a, b, c a n d d$ from $400 c m : 200 c m : : 450 c m : 3, 00, 000 c m$ as it is written $a : b : : c : d$
Here, $a = 400 c m$ $b = 200 c m$ $c = 450 c m$ $d = 3, 00, 000 c m$
Step-3: check whether $a \times d = c \times b$ or $n o t$
$a \times d = 400 \times 3, 00, 000 = 12, 00, 00, 000$
$c \times b = 450 \times 200 = 90, 000$
Here, $12, 00, 00, 000 \neq 90, 000$
$a \times d \neq c \times b$
So, $400 c m : 2 m : : 450 c m : 3 k m$ are not in proportion
Hence, The given statement is false

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