10th mathematics chapter 3 pair of linear equations in two variables optional exercise 3.7 for ncert cbse
The ages of two friends Ani and Biju differ by 3 years. Ani’s father is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Ani’s father differ by 30 years. Find the ages of Ani and Biju
let x = age of Ani
y = age of Biju
So age of Ani's father = 2x
note that Biju is elder to Cathy.
Age of Cathy = (y/2)
First assume x > y
x - y =3 -----------------(1)
[ 2x -(y/2) =30 ] *2
4x - y = 60-----------------(2)
solve (1) and (2)
x - y = 3
4x - y =60
----------------subtracting
-3x = (-57)
x = (-57) /(-3)
x=19
substitute in x - y = 3
19 - y =3
y = 19-3
y = 16
Alternately
assume y > x
so that (1) should be changed to y - x = 3
or (-x) + y =3 -------------(3)
solving (3) and (2)
(-x) + y =3
4x - y =60
------------------------adding
3x = 63
x = 63/3
x=21
substitute in (-x) + y =3 to get (-21) + y = 3
y = 3 + 21 =24
Age of Ani = 19 years and Age of Biju = 16
or
Age of Ani =21 and age of Biju =24
2. One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital?
x = original amount with the first person
y = original amount with the second person
When the second person gives the first person a 100
the first person now has (x+100) while the second person now has only (y-100)
with this in mind,
x+100 = 2(y-100)
x+100 = 2y-200
x - 2y = -200 - 100
x - 2y = (-300) -----------------(1)
when the first person gives 10 to the second person
the second person will have (y+10) while the first person will be left with (x-10)
so that
(y+10) = 6(x-10)
or
y+10 = 6x-60
-6x +y =(-70) ------------------(2)
solving (1) and (2)
x - 2y = (-300)
[-6x +y =(-70)] *2
x - 2y = (-300)
-12x +2y = (-140)
------------------------------ adding
-11x =(-440)
x = (-440)/(-11)
x = 40
substitute in x - 2y = (-300)
40 -2y = (-300)
2y = 40 +300
2y = 340
y =340/2
y=170
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ncert cbse 10th mathematics chapter 3 optional exercise 3.7
The ages of two friends Ani and Biju differ by 3 years. Ani’s father is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Ani’s father differ by 30 years. Find the ages of Ani and Biju
2. One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital?
ncert cbse 10th mathematics chapter 2 optional exercise
If the zeroes of the polynomial (x^3) – 3(x^2) + x + 1 are a – b, a, a + b, find a and b.
solution
2. Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, –7, –14 respectively
solution
4. If two zeroes of the polynomial (x^4) – 6(x^3) – 26(x^2) + 138x – 35 are
[2 ±sqrt(3) ] , find other zeroes
solution
5. If the polynomial (x^4) – 6(x^3) + 16(x^2) – 25x + 10 is divided by another polynomial (x^2) – 2x + k, the remainder comes out to be x + a, find k and a
solution
exercise 2.3
3. obtain all other zeroes of 3(x^4)+6(x^3)-2(x^2)-10x-5 if two of its zeroes are sqrt(5/3) and [sqrt(5/3)]
solution
4. On dividing (x^3) – 3(x^2) + x + 2 by a polynomial g(x), the quotient and remainder were x – 2
and –2x + 4, respectively. Find g(x).
solution
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