Question

The value of `(0.325 xx 0.325 + 0.175 xx 0.175 - 25 xx 0.00455)/(5 xx 0.0065 xx 3.25 - 7 xx 0.175 xx 0.025)`

Options

• 0.25 and 0.35

• 0.15 and 0.15

• 0.35 and 0.45

• 0.35 and 0.45

Answer 1

0.25 and 0.35

Explanation:

Given expression = `((0.325)^2 + (0.175)^2 - 25 xx 0.00455)/(5 xx 0.0065 xx 3.25 - 7 xx 0.175 xx 0.025)`

Here, 25 × 0.00455

= 5² × 5 × 7 × 13 × 10^–5

= 2 × 5 × 5² × 5 × 7 × 13 × 10^–6

= 2 ×  (5 ×  5 ×  7) ×  (52 ×  13) × 10^–6

= 2 × 175 × 325 × 10^–6

= 2 × 0.325 × 0.175

Also, 5 × 0.0065 × 3.25

= 5 × 5 × 13 × 325 × 10-6

= (0.325)²

And 7 × 0.1 75 × 0.025 = 0175 × 0.175 = (0.175)²

Hence, given expression

(where a = 0.325; b = 0.175)

= `(a^2 + b^2 - 2ab)/(a^2 - b^2)`

= `(a - b)^2/((a + b)(a - b))`

= `(a - b)/(a + b)`

= `(0.325 - 0.175)/(0.325 + 0.175)`

= `0.150/0.500`

= `15/50`

= `3/10`

= 0.30