Ratio and Proportion - ICSE STD 10 Mathematics Questions

Q 1[1 Mark Question Answer]1 Mark

Find: The reciprocal ratio of 8: 15.

View full solution →

Q 2[1 Mark Question Answer]1 Mark

Find: The sub-triplicate ratio of $216: 343$

View full solution →

Q 3[1 Mark Question Answer]1 Mark

Find: The sub-duplicate ratio of $256: 625$

View full solution →

Q 4[1 Mark Question Answer]1 Mark

Find: The triplicate ratio of $3: 7$

View full solution →

Q 5[1 Mark Question Answer]1 Mark

Find: The duplicate ratio of $7: 9$

View full solution →

Q 6[2 Mark Question Answer]2 Marks

If ax = by = cz, prove that
$\frac{x^2}{y z}+\frac{y^2}{z x}+\frac{z^2}{x y}=\frac{b c}{a^2}+\frac{c a}{b^2}+\frac{a b}{c^2}$.

View full solution →

Q 7[2 Mark Question Answer]2 Marks

Show, that a, b, c, d are in proportion if:
(6a + 7b) : (6c + 7d) : : (6a - 7b) : (6c - 7d)

View full solution →

Q 8[2 Mark Question Answer]2 Marks

If $x$ and $y$ be unequal and $x$ : $y$ is the duplicate ratio of $(x+z)$ and $(y+z)$ prove that $z$ is mean proportional between $x$ and $y$.

View full solution →

Q 9[2 Mark Question Answer]2 Marks

If $\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}$, show that each ratio is equal to $\frac{1}{2}$ or $-1.$

View full solution →

Q 10[2 Mark Question Answer]2 Marks

If $\frac{a}{b}=\frac{c}{d}=\frac{e}{f}$, Prove that each of these ratios is equal to $\frac{a+c+e}{b+d+f}$.

View full solution →

Q 11[3 marks sum]3 Marks

If a, b, c are in continued proportion, prove that $a : c = (a^2 + b^2) : (b^2 + c^2).$

View full solution →

Q 12[3 marks sum]3 Marks

If $\frac{b y+c z}{b^2+c^2}=\frac{c z+a x}{c^2+a^2}=\frac{a x+b y}{a^2+b^2}$ then show that each ratio is equal to $\frac{x}{a}=\frac{y}{b}=\frac{z}{c}$.

View full solution →

Q 13[3 marks sum]3 Marks

If (a + b + c + d) (a – b – c + d) = (a + b – c – d) (a – b + c – d), prove that a: b = c: d.

View full solution →

Q 14[3 marks sum]3 Marks

If $\frac{8 a-5 b}{8 c-5 d}=\frac{8 a+5 b}{8 c+5 d}$, prove that $\frac{a}{b}=\frac{c}{d}$.

View full solution →

Q 15[3 marks sum]3 Marks

If $a=\frac{b+c}{2}, c=\frac{a+b}{2}$ and b is mean proportional between a and c, prove that $\frac{1}{a}+\frac{1}{c}=\frac{1}{b}$.

View full solution →

Q 16[5 marks sum]5 Marks

The hypotenuse of a right angled triangle is $3 \sqrt{5}$. If the smaller side is tripled and the larger side is doubled, the new hypotenuse will be 15 cm. Find the length of each side.

View full solution →

Q 17[4 marks sum]4 Marks

If $y =\frac{\sqrt{a+3 b}+\sqrt{a-3 b}}{\sqrt{a+3 b}-\sqrt{a-3 b}}$ show that $3by^2 - 2ay + 3b = 0.$

View full solution →

Q 18[4 marks sum]4 Marks

If a, b, c, d are in continued proportion, prove that:
$\sqrt{a b}-\sqrt{b c}+\sqrt{c d}=\sqrt{(a-b+c)(b-c+d)}$

View full solution →

Q 19[4 marks sum]4 Marks

If a, b, c, d are in continued proportion, prove that $(b-c)^2+(c-a)^2+(d-b)^2=(d-a)^2$

View full solution →

Q 20[4 marks sum]4 Marks

if x =$\frac{\sqrt{a+1}+\sqrt{a-1}}{\sqrt{a+1}-\sqrt{a-1}}$ using properties of proportion show that $x^2-2 a x+1=0$

View full solution →

Q 21[4 marks sum]4 Marks

If y = $=\frac{(p+1)^{\frac{1}{3}}+(p-1)^{\frac{1}{3}}}{(p+1)^{\frac{1}{3}}-(p-1)^{\frac{1}{3}}}$ find that $y^3 - 3py^2 + 3y - p = 0.$

View full solution →

Ratio and Proportion question types

Ratio and Proportion questions

Generate a Ratio and Proportion paper free

Ratio and Proportion Mathematics - Ratio and Proportion

Ratio and Proportion question types

Ratio and Proportion questions

Generate a Ratio and Proportion paper free