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Selina solutions Selina ICSE Concise Mathematics for Class 10 chapter 7 Ratio and Proportion (Including Properties and Uses)

Chapters

Selina Selina ICSE Concise Mathematics Class 10

Selina ICSE Concise Mathematics for Class 10

Chapter 7 - Ratio and Proportion (Including Properties and Uses)

Page 0

if a : b = 5:3 find `(5a - 3b)/(5xa + 3b)`

If x: y = 4: 7, find the value of (3x + 2y): (5x + y).

If a : b = 3 : 8. Find the value of `(4a + 3b)/(6a - b)`

Find the mean proportional between `a - b and a^3 - a^2b`

If (a – b): (a + b) = 1: 11, find the ratio (5a + 4b + 15): (5a – 4b + 3).

Find the number which bears the same ratio to 

`7/33 " that "  8/21 " does to " 4/9`

If `(m + n)/(m + 3n) = 2/3` find  `(2n^2)/(3m^2 + mn)`

Find x/y when `x^2 + 6y^2 =5xy`

If the ratio between 8 and 11 is the same as the ratio of 2x - y to x + 2y. Find the value of `(7x)/(9y)`

Divide Rs 1290 in to A, B and C such that A is 2/5 of B and B:C = 4:3

A school has 630 students. The ratio of the number of boys to the number of girls is 3 : 2. This ratio changes to 7: 5 after the admission of 90 new students. Find the number of newly admitted boys.

What quantity must be subtracted from each term of the ratio 9: 17 to make it equal to 1: 3?

The work done by (x – 2) men in (4x + 1) days and the work done by (4x + 1) men in (2x – 3) days are in the ratio 3: 8. Find the value of x.

The bus fare between two cities is increased in the ratio 7: 9. Find the increase in the fare, if the original fare is Rs 245;

The bus fare between two cities is increased in the ratio 7: 9. Find the increase in the fare, if the increased fare is Rs 207.

By increasing the cost of entry ticket to a fair in the ratio 10: 13, the number of visitors to the fair has decreased in the ratio 6: 5. In what ratio has the total collection increased or decreased?

In a basket, the ratio between the number of oranges and the number of apples is 7: 13. If 8 oranges and 11 apples are eaten, the ratio between the number of oranges and the number of apples becomes 1: 2. Find the original number of oranges and the original number of apples in the basket.

In a mixture of 126 kg of milk and water, milk and water are in ratio 5 : 2. How much water must be added to the mixture to make this ratio 3 : 2?

If A: B = 3: 4 and B: C = 6: 7, find A: B: C

If A : B = 2 : 5 and A : C = 3 : 4, find A : B : C

If A: B = 3: 4 and B: C = 6: 7, find A : C

If 3A = 4B = 6C; find A: B: C.

If 2a = 3b and 4b = 5c, find: a : c.

Find the compound  ratio of 2 : 3, 9: 14 and 14: 27

Find the compound ration of `2a: 3b, mn: x^2 and x: n`

Find the compound ratio of `sqrt2: 1, 3: sqrt5` and `sqrt20: 9`

Find the duplicate ratio of 3: 4

Find the duplicate ratio of `3sqrt3: 2sqrt5`

Find the triplicate ratio of 1 : 3

Find the triplicate ration of `m/2: n/3`

Find the sub-duplicate ratio of 9: 16

Find the sub-duplicate ratio of `(x - y)^4 : (x + y)^6`

Find the sub-triplicate ratio of 64: 27

Find the sub-triplicate ratio of `x^3: 125y^3`

Find the reciprocal ratio of `x/3 : y/7`

If (x + 3) : (4x + 1) is the duplicate ratio of 3 : 5, find the value of x.

If m: n is the duplicate ratio of m + x: n + x; show that x2 = mn.

If (3x – 9) : (5x + 4) is the triplicate ratio of 3: 4, find the value of x.

Find the ratio compounded of the reciprocal ratio of 15: 28, the sub-duplicate ratio of 36: 49 and the triplicate ratio of 5: 4.

If rpq, show that p : q is the duplicate ratio of (p + r) : (q + r).

if (p - x) : (q - x) be the duplicate ratio of p : q then show that `1/p + 1/q = 1/x`

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Find the fourth proportional to 1.5, 4.5 and 3.5

Find the fourth proportional to 3a, 6a2 and 2ab2

Find the third proportional to `2 2/3 and 4`

Find the third proportional to a - b and `a^2 - b^2`

Find the mean proportional between `6 + 3sqrt3 and 8 - 4sqrt3`

If x + 5 is the mean proportional between x + 2 and x + 9; find the value of x.

If x2, 4 and 9 are in continued proportion, find x.

What number must be added to each of the numbers 6, 15, 20 and 43 to make them
proportional?

If a, b, c are in continued proportion show that `(a^2 + b^2)/(b(a + c)) = (b(a + c))/(b^2 + c^2)`

if a, b, c are in continued proportion and a(b - c) = 2b, prove that `a - c = (2(a + b))/a`

if `a/b = c/d` show that `(a^3c + ac^3)/(b^3d + bd^3) = (a + c)^4/(b + d)^4`

What least number be subtracted from each of the numbers 7, 17 and 47 so that the remainders are in continued proportion?

If y is the mean proportional between x and z; show that xy + yz is the mean proportional between x2+y2 and y2+ z2.

If q is the mean proportional between p and r, show that: pqr (p + q + r)3 = (pq + qr + rp)3

If three quantities are in continued proportion; show that the ratio of the first to the third is the duplicate ratio of the first to the second

If y is the mean proportional between x and z. prove that `(x^2 - y^2 + z^2)/(x^(-2) - y^(-2) + z^(-2)) = y^4`

Given four quantities a, b, c and d are in proportion. Show that `(a - c)b^2 : (b - d)cd = (a^2 - b^2 - ab) : (c^2 - d^2 - cd)`

Find two numbers such that the mean proportional between them is 12 and the third proportional to them is 96.

Find the third proportional to `x/y + y/x` and `sqrt(x^2 + y^2)`

If p: q = r: s; then show that: mp + nq : q = mr + ns : s.

If p + r = mq and `1/q + 1/s = m/r` then prove  that p : q = r : s

If p + r = mq and `1/q + 1/s = m/r` then prove that p : q = r : s

If `a/b = c/d` prove that each of the given ratios is equal to

`(5a + 4c)/(5b + 4d)`

If a/b = c/d prove that each of the given ratio is equal to `(13a - 8c)/(13b - 8d)`

If a/b = c/d prove that each of the given ratio is equal to `sqrt((3a^2 - 10c^2)/(3b^2 - 10d^2))`

if `a/b = c/d` prove that each of the given ratio is equal to: `((8a^3 + 15c^3)/(8b^3 + 15d^3))^(1/3)`

If a, b, c and d are in proportion prove that `(13a + 17b)/(13c + 17d) = sqrt((2ma^2 - 3nb^2)/(2mc^2 - 3nd^2)`

If a, b, c and d are in proportion prove that `sqrt((4a^2 + 9b^2)/(4c^2 + 9d^2)) = ((xa^3 - 4yb^3)/(xc^3 - 5yd^3))^(1/3)`

If `x/a = y/b = z/c` prove that `(2x^3 - 3y^3 + 4z^3)/(2a^3 - 3b^3 + 4c^3) = ((2x - 3y + 4z)/(2a - 3b + 4c))^3`

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If a : b = c : d, prove that: 5a + 7b : 5a – 7b = 5c + 7d : 5c – 7d.

If a : b = c : d, prove that: (9a + 13b) (9c – 13d) = (9c + 13d) (9a – 13b).

If a : b = c : d, prove that: xa + yb : xc + yd = b : d.

If a : b = c : d, prove that: (6a + 7b) (3c – 4d) = (6c + 7d) (3a – 4b).

Given `a/b = c/d` prove that `(3a - 5b)/(3a + 5b) = (3c - 5d)/(3c + 5d)`

If `(5x + 6y)/(5u + 6v) = (5x - 6y)/(5u - 6v)` then prove that x : y = u : v

If (7a + 8b) (7c – 8d) = (7a – 8b) (7c + 8d), prove that a: b = c: d.

if x = `(6ab)/(a = b)` find the value of `(x + 3a)/(x - 3a) = (x + 3b)/(x - 3b)`

If a = `(4sqrt6)/(sqrt2 + sqrt3)` find the value of `(a + 2sqrt2)/(a - 2sqrt2) + (a + 2sqrt3)/(a - 2sqrt3)`

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

If `(a - 2b - 3c + 4d)/(a + 2b - 3c - 4d) = (a - 2b + 3c - 4d)/(a + 2b + 3c + 4d)` show that 2ad = 3bc

If `(a^2 + b^2)(x^2 + y^2)` = (ax + by)^2 ; prove that `a/x = b/y`

If a, b, and c are in continued proportion, prove that `(a^2 + ab + b^2)/(b^2 + bc + c^2) = a/c`

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

Using properties of proportion solve for x:

`(3x + sqrt(9x^2 - 5))/(3x - sqrt(9x^2 - 5)) = 5`

Using properties of proportion solve for x 

`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`

Using properties of proportion solve for x:

`(sqrt(x + 1) + sqrt(x - 1))/(sqrt(x + 1) - sqrt(x - 1)) = (4x - 1)/2`

If x = `(sqrt(a + 3b) + sqrt(a - 3b))/(sqrt(a + 3b) - sqrt(a - 3b))` prove that `3bx^2 - 2ax + 3b = 0`

Using the properties of proportion solve for x given `(x^4 + 1)/(2x^2) = 17/8`

If `x = (sqrt(m + n) + sqrt(m - n))/(sqrt(m + n) - sqrt(m - n))` express n in terms of x and m

If `(x^2 + 3xy^2)/(3x^2y + y^3) = (m^2 + 3mn^2)/(3m^2 + n^3)` show that nx = my

Page 0

If a: b = 3: 5, find: (10a + 3b): (5a + 2b)

If 5x + 6y: 8x + 5y = 8: 9, find x: y.

If (3x – 4y): (2x – 3y) = (5x – 6y): (4x – 5y), find x: y.

Find the duplicate ratio of `2sqrt2 : 3sqrt5`

Find the triplicate ratio of 2a: 3b

Find the sub-duplicate ratio of 9x2a: 25y6b2

Find the sub-triplicate ratio of 216: 343

Find the reciprocal ratio of 3: 5

Find the ratio compounded of the duplicate ratio of 5: 6, the reciprocal ratio of 25: 42 and the sub-duplicate ratio of 36: 49.

Find the value of x, if: (2x + 3): (5x – 38) is the duplicate ratio of  `sqrt5: sqrt6`

Find the value of x, if: (2x + 1): (3x + 13) is the sub-duplicate ratio of 9: 25.

Find the value of x, if: (3x – 7): (4x + 3) is the sub-triplicate ratio of 8: 27.

What quantity must be added to each term of the ratio x: y so that it may become equal to c: d?

A woman reduces her weight in the ratio 7: 5. What does her weight become if originally it was 84 kg?

If 15(2x2 – y2) = 7xy, find x: y; if x and y both are positive.

Find the fourth proportional to 2xy, x2 and y2.

Find the third proportional to a2 – b2 and a + b.

Find the mean proportional to (x – y) and (x3 – x2y).

Find two numbers such that the mean proportional between them is 14 and third proportional to them is 112.

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.

If q is the mean proportional between p and r prove that `(p^3 + q^3 + r^3)/(p^2q^2r^2) = 1/p^3 + 1/q^3 = 1/r^3`

If a, b and c are in continued proportion, prove that: a: c = (a2 + b2) : (b2 + c2)

if x = `(2ab)/(a + b)` find the value of  `(x + a)/(x - a) + (x +b)/(x - b)`

If (4a + 9b) (4c – 9d) = (4a – 9b) (4c + 9d), prove that: a: b = c: d.

if `a/b = c/d`  show that `(a + b) : (c + d) = sqrt(a^2 + b^2) : sqrt(c^2 + d^2)`

if `x/a = y/b = z/c` prove that `(ax - by)/((a + b)(x - y)) + (by - cz)/((b + c)(y - z)) + (cz - az)/((c + a)(z - x)) = 3`

There are 36 members in a student council in a school and the ratio of the number of boys to the number of girls is 3: 1. How any more girls should be added to the council so that the ratio of the number of boys to the number of girls maybe 9: 5?

If 7x – 15y = 4x + y, find the value of x: y. Hence, use componendo and dividend to find the values of:

`(9x + 5y)/(9x - 5y)`

If 7x – 15y = 4x + y, find the value of x: y. Hence, use componendo and dividend to find the values of:

`(3x^2 + 2y^2)/(3x^2 - 2y^2)`

If `(4m + 3n)/(4m - 3n) = 7/4` use properties of proportion to find m : n

If `(4m + 3n)/(4m - 3n) = 7/4` use properties of proportion to find `(2m^2 - 11n^2)/(2m^2  + 11n^2)`

If x, y, z are in continued proportion prove that `(x + y)^2/(y + z)^2 = x/z`

Given x = `(sqrt(a^2 + b^2) + sqrt(a^2 - b^2))/(sqrt(a^2 + b^2) + sqrt(a^2 - b^2))`

Use componendo and dividendo to prove that b^2 = (2a^2x)/(x^2 + 1)

If `(x^2 + y^2)/(x^2 - y^2) = 2 1/8` find `x/y`

if `(x^2 + y^2)/(x^2 - y^2) = 2 1/8` find `(x^3 + y^3)/(x^3 - y^3)`

Using componendo and dividendo find the value of x

`(sqrt(3x + 4) + sqrt(3x - 5))/(sqrt(3x + 5) - sqrt(3x - 5)) = 9`

If `x = (sqrt(a + 1) + sqrt(a - 1))/(sqrt(a + 1) + sqrt(a - 1))`, using properties of proportion show that `x^2 - 2ax + 1 = 0`

Given `(x^3 + 12x)/(6x^2 + 8) = (y^3 + 27y)/(9y^2 + 27)`  using componendo and divendo find x : y

Selina Selina ICSE Concise Mathematics Class 10

Selina ICSE Concise Mathematics for Class 10
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