RD Chapter 3 Pair of Linear Equations in Two Variables Ex 3.11 Solutions
Question - 21 : - The students of a class are made to stand in rows. If 3 student are extra in a row, there would be 1 row less. If 3 students are less in a row there would be 2 rows more. Find the number of students in the class.
Answer - 21 : -
Let number of rows = x
and number of students in each row = y
Now according to the conditions given
Number of total students = xy
(y + 3)(x – 1) = xy
=> xy – y + 3x – 3 = xy
=>3x – y = 3 …(i)
and (y – 3) (x + 2) = xy
=> xy + 2y – 3x – 6 = xy
=> 2y – 3x = 6 …(ii)
Adding (i) and (ii), y = 9
Substituting the value of y in (i)
3x – 9 = 3
=> 3x = 3 + 9 = 12
=> x = 4
Number of total students = xy = 4 x 9 = 36
Question - 22 : - One says, “give me 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 ?
Answer - 22 : -
Let first person has amount of money = Rs. x
and second person has = Rs. y
Now according to the conditions given,
x + 100 = 2(y – 100)
=> x + 100 = 2y – 200
=> x – 2y = – 200 – 100
=> x – 2y = -300 ………(i)
and 6(x – 10) = (y + 10)
=> 6x – 60 = y + 10
=> 6x – y = 10 + 60
=> 6x – y = 70 ……….(ii)
From (i), x = 2y – 300
Substituting the value of x in (ii)
6(2y – 300) – y = 70
=> 12y – 1800 – y = 70
=> 11y = 70 + 1800 = 1870
y = 170
x = 2y – 300 = 2 x 170 -300 = 340 – 300 = 40
First person has money = ₹ 40
and second person has = ₹ 170
Question - 23 : - A shopkeeper sells a saree at 8% profit and a sweater at 10% discount, thereby getting a sum of ₹ 1008. If she had sold the saree at 10% profit and the sweater at 8% discount, she would have got ₹ 1028. Find the cost price of the saree and the list price (price before discount) of the sweater. [NCERT Exemplar]
Answer - 23 : - Let the cost price of the saree and the list price of the sweater be ₹ x and ₹ y, respectively.
Question - 24 : - In a competitive examination, one mark is aw awarded for each correct answer while 1/2 mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly. [NCERT Exemplar]
Answer - 24 : -
Let x be the number of correct answer of the questions in a competitive examination,
then (120 – x) be the number of wrong answers of the questions.
Then, by given condition,
Hence, Jayanti answered correctly 100 questions.
Question - 25 : - A shopkeeper gives books pn rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Latika paid ₹ 22 for a book kept for 6 days, while Anand paid ₹ 16 for the book kept for four days. Find the fixed charges and charge for each extra day. [NCERT Exemplar]
Answer - 25 : -
Let Latika takes a fixed charge for the first two day is ₹ x and additional charge for each day thereafter is ₹ y.
Now, by first condition,
Latika paid ₹ 22 for a book kept for six days
i.e., x + 4y = 22 …(i)
and by second condition,
Anand paid ₹ 16 for a book kept for four days
i.e., x + 2y = 16 …(ii)
Now, subtracting Eq. (ii) from Eq. (i), we get
2y = 6 => y = 3
On putting the value of y in Eq. (ii), we get
x + 2 x 3 = 16
x = 16 – 6 = 10
Hence, the fixed charge = ₹ 10
and the charge for each extra day = ₹ 3