Ratio and Proportion
Question
Q1.
Gold and copper are melted together in the ratio of 7 : 4 . what is the weight of melted mixture if 15 kg o gold has been consumed
in it .
Solution.
7/4
=
15/x
⇒ x = 8.57 kg
so total weight of melted mixture = 23.57
Solution
Q2.
Find the fourth proportional to 4x . x2, y
let a is the fourth proportional
4x : x
2 = y : a ⇒
4x/x2
=
y/a
⇒
4/x
=
y/a
a =
xy/4
Q3.
If p:q is the sub-duplicate ratio of p - x2 : q - x2 then x is
Solution.
sub-duplicate ratio of p - x
2 : q - x
2 is √( p - x
2) : √( q - x
2)
√( p - x2)/√(q - x2)
=
p/q
on squaring both sides
p - x2/ q - x2
=
p2/q2
on solving
this we get
x = √(
pq/p+q
)
Solution
Q4.
A jar contains red and green balls , there are 10 balls in a jar, then which ratio will not be suitable .
(a) 7:3 (b) 9:1 (c) 1:11 (d) 1:4
Solution.
(c) 1:11 = this shows 12 balls.
Solution
Q5.
If p/4 = q/5 = r/9 , then (p+q+r)/p is .
(a) 3.5 (b) 4.5 (c) 4 (d) 5
Solution.
p/4 = q/5 = r/9 = k
p = 4k , q = 5k , r = 9k
= (4k+5k+9k)/4k
= 18k/4k
= 18/4 = 18/4
9/2 = 4.5
Solution
Q6.
A began a business with Rs. 900 and joined after wards by B with Rs.600 for how many months B was in business if at the end of the year profit
divided in the ratio of 2:1 ?
(a) 7 months (b) 9 months (c) 6 months (d) 8 months
Solution.
A's capital x A's time/B's capital x B's time
=
A's profit/B's profit
900 x 12/600 x (x)
=
2/1
900 x 12 = 1200x
900 = 100x
x = 9
Solution
Q7.
Write the subtriplicate ratio of 125:27.
(a)5:3 (b) 3:2 (c) 2:1 (d) 4:3
Solution.
(a)5:3
NOTE :
Subtriplicate ratio of a and b is ∛a : ∛b
Solution
Q8.
In 60 litres mixture of milk and water the ratio of milk and water is 7:3. Find the quantity of water to be added in the mixture in order
to make this ratio 3:7 .
(a) 20 litre (b) 80 litre (c) 40 litre (d) 10 litre
Solution.
= 42/18
42/(18 + x) = 3/7
294 = 54 + 3x
240 = 3x
x = 80
Solution
Q9.
If x1/3 + y1/3 + z1/3 = 0 , find the value of (x+y+z)3 .
(a) 1 (b) 3xyz
(c) 27xyz (d) xyz
Solution.
x1/3 + y1/3 + z1/3 = 0
(x1/3)3 + (y1/3)3 +
(z1/3)3 = 3x1/3.y1/3.z1/3
x + y + z = 3x1/3.y1/3.z1/3
(x + y + z)3 = (3x1/3.y1/3.z1/3)3 = 27xyz
Note : If x + y + z = 0 then x3 + y3 + z3 = 3abc
Solution
Q10.
If A:B = 1:2, B:C = 3:4 and C:D = 5:6, find A:B:C:D .
(a) 15:30:40:48 (b) 3:2:6:10 (c) 9:18:15:20
(d) 19:20:21:22
Solution.
A:B = 1:2
B:C = 3:4
= 2:(8/3)
C:D = 5:6
= (8/3):(16/15)
A:B:C:D = 1:2:(8/3):(16/15)
= 15:30:40:48
Solution
