Advertisements
Advertisements
Question
If r2 = pq , show that p : q is the duplicate ratio of (p+r) : ( q+r)
Advertisements
Solution
`"p"/"q" = ("p + q")^2/("q + r")^2`
`=> "p"/"q" = ("p"^2 + "r"^2 + 2"pr")/("q"^2 + "r"^2 + 2"qr")`
`=> "p"/"q" = ("p"^2 + "pq" + 2"pr")/("q"^2 + "pq" + 2"qr")`
⇒ pq2 +p2q+ 2pqr -p2q+pq2 + 2pqr
Since LHS = RHS, therefore p:q 1s the duplicate ratio of (p + r) : (q + r) .
APPEARS IN
RELATED QUESTIONS
Find the ratio of the speed of a cycle 15 km per hour to the speed of scooter 30 km per hour.
A school has 630 students. The ratio of the number of boys to the number of girls is 3 : 2. This ratio changes to 7 : 5 after the admission of 90 new students. Find the number of newly admitted boys.
A cistern of milk caitains a mixture of milk and water in the ratio of 11 :4. If the cistern contains 60 litres of milk, how much more water must be added to make the
ratio of milk to water as 11:6 ?
Find: The duplicate ratio of 7: 9
If (4x2 + xy) : (3xy – y2) = 12 : 5, find (x + 2y) : (2x + y).
Find the following ratio in the simplest form:
4 kg to 750 g
Mr. Sahai and his wife are both school teachers and earn Rs 16800 and Rs 10500 per month respectively. Find the ratio of
(i) Mr. Sahai's income to his wife's income;
(ii) Mrs. Sahai's income to her husband's income;
(iii) Mr. Sahai's income to the total income of the two.
If a bus covers 195 km in 3 hours and a train covers 300 km in 4 hours, then the ratio of their speeds is
Present age of father is 42 years and that of his son is 14 years. Find the ratio of Present age of father to the present age of son.
In a school excursion, 6 teachers and 12 students from 6th standard and 9 teachers and 27 students from 7th standard, 4 teachers and 16 students from 8th standard took part. Which class has the least teacher to student ratio?
