Question

Select the appropriate alternative answer for the following questions.

(i) If 6 : 5 = y : 20 then what will be the value of y ?

(A) 15 (B) 24 (C) 18 (D) 22.5

(ii) What is the ratio of 1 mm to 1 cm ?

(A) 1 : 100 (B) 10 : 1 (C) 1 : 10 (D) 100 : 1

(iii * ) The ages of Jatin, Nitin and Mohasin are 16, 24 and 36 years respectively. What is the ratio of Nitin’s age to Mohasin’s age ?

(A) 3 : 2 (B) 2 : 3 (C) 4 : 3 (D) 3 : 4

(iv) 24 Bananas were distributed between Shubham and Anil in the ratio 3 : 5, then how many bananas did Shubham get ?

(A) 8 (B) 15 (C) 12 (D) 9

(v) What is the mean proportional of 4 and 25 ?
(A) 6 (B) 8 (C) 10 (D) 12

Answer 1

(i)
6 : 5 = y : 20

$$\begin{gathered} \therefore \frac{6}{5}=\frac{y}{20} \\ \Rightarrow y=\frac{6\times 20}{5}=24 \end{gathered}$$
Thus, the value of y is 24.

Hence, the correct answer is option (B).

(ii)
Ratio of 1 mm to 1 cm

= 1 mm : 1 cm

= 1 mm : 10 mm (1 cm = 10 mm)

= 1 : 10

Hence, the correct answer is option (C).

(iii)
Age of Nitin = 24 years

Age of Mohasin = 36 years

∴ Ratio of Nitin's age to Mohansin's age

= Age of Nitin : Age of Mohasin

= 24 years : 36 years

$$\begin{gathered} =\frac{24}{36} \\ =\frac{24÷12}{36÷12}\left(\mathrm{HCF}\mathrm{of}24\mathrm{and}36=12\right) \\ =\frac{2}{3} \end{gathered}$$
= 2 : 3

Thus, the ratio of Nitin's age to Mohasin's age is 2 : 3.

Hence, the correct answer is option (B).

(iv)
The number of bananas received by Shubham and Anil is the ratio 3 : 5.

Let the number of bananas received by Shubham and Anil be 3x and 5x, respectively.

∴ 3x + 5x = 24

⇒ 8x = 24

⇒ x = 3

∴ Number of bananas received by Shubham = 3x = 3 × 3 = 9

Thus, Shubham gets 9 bananas.

Hence, the correct answer is option (D).

(v)
Mean proportional of 4 and 25

$$\begin{gathered} =\sqrt{4\times 25} \\ =\sqrt{100} \\ =10 \end{gathered}$$
Thus, the mean proportional of 4 and 25 is 10.

Hence, the correct answer is option (C).