Class 10 ICSE Maths Chapter Ratio&Proportion
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class 10 Ratio&Proportion Exercise7-1
Ratio and Proportion
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Q1 Find the value of x in the following proportions:
(i) 10: 35 = x: 42
(ii) 3: x = 24: 2
(iii) 2.5: 1.5 = x: 3
(iv) x: 50 :: 3: 2
Q2 Find the fourth proportional to
(i) 3, 12, 15
(ii) 1/3, 1/4, 1/5
(iii) 1.5, 2.5, 4.5
(iv) 9.6 kg, 7.2 kg, 28.8 kg
Q3 Find the third proportional to
(i) 5, 10
(ii) 0.24, 0.6
(iii) ₹ 3, ₹ 12
(iv) 5 ¼ and 7
Q4 Find the mean proportion of:
(i) 5 and 80
(ii) 1/12 and 1/75
(iii) 8.1 and 2.5
(iv) (a - b) and (a3 - a2b), a ˃ b
Q6 What number must be added to each of the numbers 5, 11, 19 and 37 so that they are in proportion?
Q7 What number should be subtracted from each of the numbers 23, 30, 57 and 78 so that the remainders are in proportion?
Q10 What number must be added to each of the numbers 16, 26 and 40 so that the resulting numbers may be in continued proportion?
Q11 Find two numbers such that the mean proportional between them is 28 and the third proportional to them is 224
Q12 If b is the mean proportional between a and c, prove that a, c, a2 + b2 and b2 + c2 are proportional
Q13 If b is the mean proportional between a and c, prove that (ab + bc) is the mean proportional between (a2 + b2) and (b2 + c2)
Q14 If y is mean proportional between x and z, prove that xyz (x + y + z)3 = (xy + yz + zx)3
Q16 If x/a = y/b = z/c, prove that
(i) x3 / a2 + y3 / b2 + z3 / c2 = (x+y+z)3 / (a+b+c)2
(ii) [ a2x2+b2y2+c2z2 / a3x+b3y+c3z ]3 = xyz / abc
(iii) ax-by / (a+b)(x-y) + by-cz / (b+c)(y-z) + cz-ax / (c+a)(z-x) =3
Q17(i) If a/b = c/d = e/f prove that: (i) (b2 + d2 + f2) (a2 + c2 + e2) = (ab + cd + ef)2
Q17(iii) If a/b = c/d = e/f prove that: a2 / b2 + c2 / db2 + e2 / f2 = ac / bd + ce / df + ae / df
Q17(iv) If a/b = c/d = e/f prove that:
bdf[ a+b / b + c+d / d + c+f / f ]3 = 27(a+b)(c+d)(e+f)
Q18 If ax = by = cz; prove that:
x2 / yz + y2 / zx + z2 / xy = bc / a2 + ca / b2 + ab / c2
Q19(i) If a, b, c and d are in proportion, prove that:
(5a + 7v) (2c - 3d) = (5c + 7d) (2a - 3b)
Q19(iii) If a, b, c and d are in proportion, prove that:
(a4 + c4): (b4 + d4 ) = a2c2: b2d2
Q21 If a, b, c are in continued proportion, prove that:
pa2+qab+rb2 / pb2+qbc+rc2 = a / c
Q22(i) If a, b, c are in continued proportion, prove that:
a+b / b+c = a2(b-c) / b2(a-b)
Q22(ii) If a, b, c are in continued proportion, prove that:
1 / a3 + 1 / b3 + 1 / c3 = a / b2c2 + b / c2a2 + c / a2b2
Q22(iii) If a, b, c are in continued proportion, prove that: a: c = (a2 + b2): (b2 + c2)
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