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NCERT Exemplar Solutions Class 8 Mathematics Solutions for Rational Numbers - Exercise in Chapter 1 - Rational Numbers

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Question 318 Rational Numbers - Exercise
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A mother and her two daughters got a room constructed for ₹ 62,000. The elder daughter contributes 3/8 of her mother’s contribution while the younger daughter contributes ½ of her mother’s share. How much do the three contribute individually?

Answer:

From the question it is given that,

A mother and her two daughters got a room constructed for = ₹ 62,000

Let us assume mother’s share be x,

Then,

The elder daughter’s contribute = 3/8 of her mother’s share

= 3/8 x

The younger daughter’s contribute = ½ of her mother’s share

= ½ x

So, mother’s share + elder daughter’s share + younger daughter’s share = ₹ 62,000

x + (3/8) x + ½ x = ₹ 62,000

The LCM of the denominators 1, 8 and 2 is 8

(1/1) = [(1×8)/ (1×8)] = (8/8)

(3/8) = [(3×1)/ (8×1)] = (3/8)

(1/2) = [(1×4)/ (2×4)] = (4/8)

Then,

(8/8) x + (3/8) x + (4/8) x = 62,000

(8x + 3x + 4x)/8 = 62,000

(15x/8) = 62,000

15x = 62,000 × 8

X = 496000/15

X = ₹ 33,066.6

∴Mother’s share = ₹ 33,066.6

Elder daughter’s share = 3/8 of her mother’s share

= 3/8 x

= 3/8 × 33066.6

= ₹ 12,400

Younger daughter’s share = ½ of her mother’s share

= ½ x

= ½ × 33066.6

= ₹ 16,533.3

Video transcript
"hello students welcome to lido homework let us solve the question which is given on the screen today it reads a mother and her two daughters got a room constructed and the cost of the room is given as 62 000 rupees now the elder daughter contributes three eighth of her mother's contribution okay of how much her mother contributed out of which three eighth part that much amount the elder daughter contributed while the younger daughter contributes one by two of her mother's shares again so how much do the three contribute individually so this is a clear word problem and you can use a formation of linear equation and then solve it to get the amount of share that each one contributed so let us see how we can do this we can first take since both the daughter's share is compared with the mother's share which we don't know so let us take mother share as x for more clarity okay so let mother share be rupees x is equal to rupees x okay so elder daughter share is how much elder daughter share is how much it is 3 8 of her mother's contribution that's what is written here okay so it is 3 by 8 her mother contribution is x so this becomes 3 by x three by eight x rupees okay now younger daughter contribution [Music] younger daughter contribution is equal to how much as per the given information she shares half of how much her mother share so this becomes half of x rupees so when we now have the amount shared by all the three people okay now it is also given the total amount is 62. so if we add all the three amounts it should be sorry 62 000. so let us add all the three x plus 3 by 8 x plus 1 by 2 x when you add all the 3 shares it is 62 000. so this is simple linear equation we need to solve them to solve it since all the three terms are x term we are taking excess common and adding the coefficients separately 1 plus 3 by 8 plus 1 by 2 is equal to 62 000 so this can be further simplified as x and 2 here the denominator the lcm of eight and two is eight so this numerator becomes eight plus three plus two fours are eight so one fours of four is equal to sixty two thousand this can be further simplified as x into fifteen by 8 is equal to 62 000 so now we'll take the 15 by 8 on the right hand side here it is multiplying there it will divide so there also it can multiply by its reciprocal according to the rule of division 62 000 into 8 by 15 so when you simplify it you get the value of x as rupees 3 three zero six six point six six okay so this is the amount her mother has shared because x value is this much so that is the mother's share we need to calculate both the daughter's share now so let us do that here so you can write it as i'm just writing d1 or elder daughter share is equal to 3 by 8 into it is 33066.66 so when you calculate you're getting the value as rupees 1 12 400 so that is the elder daughter share now the younger daughter share is 1 by 2 of 33066.6 which will give the answer as rupees 16533 now the mother share we already know so i'll just put an arrow and write mother okay i hope it's clear if you still have any doubt put a message in the comment section and subscribe to our channel for regular updates bye "
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