Class 10 ICSE Maths Ratio and Proportions Important Questions
Ratio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of a:b, then it is a ratio whereas a proportion states that two ratios are equal. Here, a and b are any two integers. The ratio and proportion are the two important concepts, and it is the foundation to understand the various concepts in mathematics as well as in science
Class 10 ICSE Ratio and Proportios Important Questions
Ratio and Proportions Important Questions
Q.1 Two numbers are in the ratio 3 : 5. If 8 is added to each number, the ratio becomes 2 : 3. Find the numbers.
Solution
Q2 The work done by (x - 3) men in (2x + 1) days and the work done by (2x + 1) men in (x + 4) days are in the ratio 3 : 10. Find the value of x.
Solution
Q3 If a/b+c = b/c+a = c/a+b and a + b + c ≠ 0 ; show that each given ratio is equal to 1/2 .
Solution
Q4 Find the ratio compounded of the duplicate ratio of 5 : 6, the reciprocal ratio of 25 : 42 and the sub-triplicate ratio of 216 : 343.
Solution
Q5
Find :
(i) the fourth proportional to 3, 6 and 4.5.
(ii) the mean proportional between 6.25
and 0.16.
(iii) the third proportional to 1.2 and 1.8.
Solution
Q6
What should be added to each of the numbers 13, 17 and 22 so that the resulting numbers are in
continued proportion ?
Solution
Q7
If (a2 + c2), (ab + cd) and (b2 + d2) are in continued
proportion; prove that a, b, c and d are in proportion.
Solution
Q8
If q is the mean proportional between p and r, prove that :
p2 - q2 + r2 = q4 (
1
/
p2
-
1
/
q2
+
1
/
r2
)
Solution
Q9
If
8x + 13y
/
8x - 13y
=
9
/
7
, find x : y
Solution
Q10
If
8a - 5b
/
8c - 5d
=
8a + 5b
/
8c + 5d
, prove that
a
/
b
=
c
/
d
Solution
Solution
Q11
If p=
4xy
/
x + y
, find the value of
p + 2x
/
p - 2x
+
p + 2y
/
p - 2y
Solution
Q12
If x =
√(3a + 2b) + √(3a - 2b)
/
√(3a + 2b) - √(3a - 2b)
, prove that bx2 - 3ax + b = 0
Solution
Q13
Using properties of proportion solve for x , given
x4 + 1
/
2x2
=
17
/
8
Solution
Q14
If x =
√(m + n) + √(m - n)
/
√(m + n) - √(m - n)
, express n in terms of x and m.
Solution
Q15
Find the third propotional to
x
/
y
+
y
/
x
and √x2 + y2
Solution
Q16
If p : q = r : s; then show that :
mp + nq : q = mr + ns : s.
Solution
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