Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
Find : (i) the fourth proportional to 4, 9, 12 ; \item[(ii)] the third proportional to 16 and 36 ; \item[(iii)] the mean proportional between 0.08 and 0.18 ; \item[(iv)] the mean proportional between $6+3 \sqrt{3}$ and $8-4 \sqrt{3}$.
Answer
Answer (as printed):
Explanation
(i) Let the fourth proportional to 4, 9, 12 be x. 9 × 12 Then, 4 : 9 : : 12 : x ⇔ 4 × x = 9 × 12 ⇔ x = = 27. 4 \ Fourth proportional to 4, 9, 12 is 27. (ii) Let the third proportional to 16 and 36 be x. 36 × 36 Then, 16 : 36 : : 36 : x ⇔ 16 × x = 36 × 36 ⇔ x = = 81. 16 \ Third proportional to 16 and 36 is 81. (iii) Mean proportional between 0.08 and 0.18 8 18 144 12 = 0.08 × 0.18 = × = = = 0.12. 100 100 100 × 100 100 (iv) Mean proportional between 6 + 3 3 and 8 – 4 3 = (6 + 3 3) (8 – 4 3) = 48 – 36 = 12 = 2 3.
Explanation as extracted from the printed page; notation may be imperfect.