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Ratio and Proportion

Q1. If
x2 + y2/ x2 - y2
=
10/6
, find x : y

(a) 2 : 1

(b) 1 : 3

(c) 3 : 2

(d) 4 : 2

Solution. a
Using componendo and dividendo

(x2 + y2) + (x2 - y2)/ (x2 + y2) - (x2 - y2)
=
10 + 6/10 - 6


2x2/2y2
=
16/4
⇒
x2/y2
=
16/4
⇒
x/y
= 2

x:y = 2:1
Solution

Q2. If x:y = 5:4 , find
x3 + y3/ x3 - y3


(a)
4/9


(b)
189/61


(c)
39/41


(d)
1000/127

Solution.a
x/y
=
5/4
⇒
x3/y3
=
125/64


Now , using componendo and dividendo

x3 + y3/ x3 - y3
=
125 + 64/125 - 64
=
189/61
Solution

Q3. A ratio equivalent to the ratio
2/3
:
5/7


(a) 16:19

(b) 4:9

(c) 14:15

(d) 2:3

Solution. c
L.C.M of 3 and 7 = 21

2 x 21/3
:
5 x 21 /7
= 14 : 15
Solution

Q4. Find the duplicate ratio of 2:9

(a) 4:81

(b) 2:81

(c) 3:9

(d) 4:25

Solution.a
∴ Duplicate ratio of a:b is a2 : b2
Solution

Q5. Find the sub - triplicate ratio of 27:64 .

(a) 2:4

(b) 3:4

(c) 1:4

(d) 9:10

Solution. b
∴ Sub - triplicate ratio of ∛a : ∛b
Solution