Advertisements
Advertisements
Question
If p + r = 2q and `(1)/q + (1)/s = (2)/r`, then prove that p : q = r : s.
Advertisements
Solution
`(1)/q + (1)/s = (2)/r`
⇒ `(s + q)/(qs) = (2)/r`
⇒ 2qs = r(s + q)
⇒ (p + r)s = r(s + q)
⇒ ps + rs = rs + rq
⇒ ps = rq
⇒ `p/q = r/s`.
Hence proved.
RELATED QUESTIONS
Find triplicate ratio of 1 : 3
Find the ratio compounded of the duplicate ratio of 5 : 6, the reciprocal ratio of 25 : 42 and the sub-duplicate ratio of 36 : 49.
Find the compounded ratio of the following:
(m-n):(m+n), (m+n)2 : (m2+n2) and (m4 - n4): (m2-n2) 2
Find the reciprocal ratio of e following :
81pq2 : 54p2q
Find the compound ratio of the following:
If P : Q = 6 : 7, Q : R = 8 : 9 find P : Q : R.
In winter, a school opens at 10 a.m. and closes at 3.30 p.m. If the lunch interval is of 30 minutes, find the ratio of lunch interval to total lime of the class periods.
Express the following ratio in the simplest form:
324 : 144
|
Distance from Mary’s home to school (in km.)
|
10 | 4 | |||
|
Distance from John’s home to school (in km.)
|
5 | 4 | 3 | 1 |
Out of 50 students in a class, 30 are boys. Find the ratio of number of girls to the total number of students
Out of 1800 students in a school, 750 opted basketball, 800 opted cricket and remaining opted table tennis. If a student can opt only one game, find the ratio of number of students who opted basketball to the total number of students.
