Question

Fill in the blanks.

(i) 3 : 4 = (......)%
(ii) 0.75 = (......)%
(iii) 6% = ...... (express in decimals)
(iv) If x decreased by 40% gives 135, then x = ...... .
(v) (11% of x) − (7% of x) = 18 ⇨ x = ......

Answer 1

We have the following:

(i) 3 : 4 = (75)%
Explanation: 3 : 4 = $\frac{3}{4}$ = $\left(\frac{3}{4}\times 100\right)\%=\left(3\times 25\right)\%=75\%$

(ii) 0.75 = (75)%
Explanation: ( 0.75 $\times$ 100)% = 75%


(iii) 6% = 0.06 (expressed in decimals)
Explanation: 6% = $\frac{6}{100}=0.06$

(iv) If x decreased by 40% gives 135, then x = 225
Explanation:
Let the number be x.
According to question, we have:
x − 40% of x = 135
⇒ $\left(x-\frac{40x}{100}\right)=135$
⇒ $\left(\frac{100x-40x}{100}\right)=135$
⇒ $\left(\frac{60x}{100}\right)=135$
⇒ x = $\left(\frac{135\times 100}{60}\right)$ = 225

(v) (11% of x) − (7% of x) = 18
⇒ x = 450
Explanation:
(11% of x) − (7% of x) = 18
⇒ $\left(\frac{11x}{100}-\frac{7x}{100}\right)=18$
⇒ $\frac{4x}{100}=18$
∴ x = $\left(\frac{18\times 100}{4}\right)=\left(18\times 25\right)=450$