State whether the following statement is true or false
$2 l 140 m l : 1 l 70 m l : : 550 g : 1 k g 400 g$

True

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False

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Solution

The correct option is B False
Step-1: Convert $2 l 140 m l, 1 l 70 m l i n t o m l$ and $1 k g 400 g i n t o g$
$2 l 140 m l = 2 \times 1000 + 140 = 2000 + 140 = 2140 m l$ ( As $1 l = 1000 m l$ )
$1 l 170 m l = 1 \times 1000 + 70 = 1000 + 70 = 1070 m l$ ( As $1 l = 1000 m l$ )
$1 k g 400 g = 1 \times 1000 + 400 = 1000 + 400 = 1400 g$ ( As $1 k = 1000 g$ )
Now, $2 l 140 m l : 1 l 70 m l : : 550 g : 1 k g 400 g$ equivalent to $2140 m l : 1070 m l : : 550 g : 1400 g$
Step-2: write $a, b, c a n d d$ from $2140 m l : 1070 m l : : 550 g : 1400 g$ as it is written $a : b : : c : d$
Here, $a = 2140 m l$ $b = 1070 m l$ $c = 550 g$ $d = 1400 g$
Step-3: check whether $a \times d = c \times b$ or $n o t$
$a \times d = 2140 \times 1400 = 29, 96, 000$
$c \times b = 1070 \times 2140 = 22, 89, 800$
Here, $29, 96, 000 \neq 22, 89, 800$
$a \times d \neq c \times b$
So, $2 l 140 m l : 1 l 70 m l : : 550 g : 1 k g 400 g$ are not in proportion
Hence, the given statement is false.

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