Framing Relations

Q. Solve the following.
Shabana scored 736 marks out of 800 in her exams. What was the percentage she scored?

Q. A father said to his son, "I was as old as you are at the present, at the time of your birth". If the father's age is 38 years now, the son's age five years back was:

1. 10 years
2. 12 years
3. 14 years
4. 19 years

Q.

An autorickshaw charges Rs. 10 for the first kilometre then Rs. 8 for each such subsequent Kilometre. The total charge (in Rs) for d kilometres is

1. 8 + (d - 1)10
2. (d - 1)8
3. 10 + (d - 1)8
4. 10 + (d)8

Q.

If $a,b$ and $c$ are real numbers, such that $a+2b+4c=0$. Then, the equation $a{x}^2+bx+c=0$

1. has both the roots complex

2. has its roots lying within $–1<x<0$

3. has one of the roots equal to $\frac{1}{2}$

4. has its roots lying within $2<x<6$

Q.

Rahul's father age Is 5 more than the 3 times his age. If its father age is 35 year, find the age of Rahul.

1. 12 years

2. 15 years

3. 5 years

4. 10 years

Q. Ram has some marbles, if Shyam has 5 more marbles than Ram has, then find the number of marbles Ram and Shyam have respectively(use any letter for number of marbles).

1. y, y + 5
2. p - 5, p
3. y, 5 - y
4. p, 5p

Q.

How do you solve for $y$ for the equation $2x-3y=6$?

Q. Mr. Bose gave 2/3 of his money to his wife. His wife gave 3/4 of her money to her daughter. 2/3 of her daughter's money was stolen and she was left with ruppees 30000. How much money did Mr Bose had?

Q.

Frame an expression - Three less than half of a number.

1. $\frac{x}{2}-3$

2. $2x-3$

3. $\frac{x}{3}-3$

4. $\frac{x}{4}-3$

Q.

A piece of wire $\frac{7}{8}$ metre long broke into two pieces. One piece was $\frac{1}{4}$ metre long. How long is the other piece?

1. $\frac{5}{10}$ metre
2. $\frac{5}{8}$ metre
3. $\frac{2}{8}$ metre
4. $\frac{6}{7}$ metre

Q.

If the cost of 1 pencil is Rs. x , then the cost of 10 pencils is

1. x/10

2. x + 10

3. 10x

4. x - 10

Q.

When $5$ is added to a number, we get $15$. How do we represent this in the form of an equation in variable $x$?

1. $x=15+5$

2. $x-5=15$

3. $x+5=15$

4. $x+15=5$

Q.

Frame an equation - The product of two consecutive numbers is 110.

1. x(x + 2) = 110

2. 2x(x + 1) = 110

3. x(x + 1) = 110

4. 2x(x + 2) = 110

Q.

Rahul's age is five more than twice of his son's age. If the son's age is 'x' years, then Rahul's age can be expressed as:

1. 2x - 5

2. x + 5

3. x + 10

4. 2x + 5

Q.

Jenny is $9$ years younger than Sammie.

Five years ago Sammie was $4$ times older than Jennie.

How old is each now?

Q.

Raj takes $2\frac{1}{2}$ hours to complete his homework. However, Seema takes $\raisebox{1ex}{$8$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ hours to complete her homework.Who takes less time and by how much $?$

Q. Anju went to a fair one day. The entry fee to the fair was Rs 10 and each game cost Rs 5 to play. If the number of games played by Anju is x, what is the expression for the total amount spent?

1. $10x+5$
2. $5(x+10)$
3. $10(x+5)$
4. $5x+10$

Q.

Translate each of the following statements into equations.

The selling price$\left(s\right)$ of an item is equal to the sum of the cost price$\left(c\right)$of an item and the profit (p) earned.

Q.

The solution of the equation $x+15=19$ is __________

Q.

Change the statement using expression into statement in ordinary language .

Our class has $\mathrm{n}$ students. The school has $20\mathrm{n}$ students.

Q. Autos in Bangalore have a fixed charge of Rs. 25 for the first 2 km and then an additional charge of Rs.13 per each additional km. If $x$ represents the distance travelled, find an expression for the total charge.

Q.

One store got $1.2$ times as much apple cider as the second store.

Every hour the first store was selling $90$ liters of cider, while the second one was selling $80$ liters per hour.

In $2.5$ hours the second store had $65$ liters less than the first store.

How many liters of cider were delivered to each store $?$

Q.

Frame an equation: Sum of two consecutive numbers is 27.

1. x + 1 = 27

2. x + 2 = 27

3. 2x + 2 = 27

4. 2x + 1 = 27

Q.

Autos in Bangalore have a fixed charge of Rs. 25 for the first 2 km and then an additional charge of Rs.13 per each additional km. If $x$ represents the distance travelled, find an expression for the total charge.

1. 13$x$ + 1
2. 13$x$ - 1
3. 25 + 13$x$
4. None of these

Q. The number of pencils bought by Shilpa from a shop is p. If Devi buys four times as many pencils as Shilpa bought and 30 pencils remained in the shop after the purchase, then which expression gives the number of pencils initially present in the shop?

1. p + 30
2. 5p + 30
3. 4p + 30
4. 5p - 30

Q.

There are $m$ boxes in a large bag and $n$ toys in each box. How many toys are present in the bag ?

1. $m+n$

2. $m-n$

3. $mn$

4. $\frac{m}{n}$

Q. Four-fifths of a number is 10 more than two-thirds of the number. Find the number.

Q. The monthly income of A and B are in the ratio 3:4 and their monthly expenditures are in the ratio 7:11. If each saves Rs. 2500 per month, find the monthly income of each.

Q. Total wages, ₹W of a man includes basic wage of ₹B, for t hours week, plus ₹R per hour over time. Frame an algebraic expression for the wages of the man if he works a total of T hours.

Q. Manish and Nitish are brothers. Manish is three years younger than Nitish. If Nitish age is $x$ then Manish’s age could be represented by the algebraic expression.
$\left[2Marks\right]$