Question 2 :
Solve 10x – 5 – 7x = 5x + 15 – 8.
Question 4 :
State whether the statement is TRUE or FALSE : A and B are together 90 years old. Five years ago A was thrice as old as B was. Hence, the ages of A and B five years back would be (x – 5) years and (85 – x) years respectively.
Question 5 :
The perimeter of a rectangle is 240 cm. If its length is increased by 10% and its breadth is decreased by 20%, we get the same perimeter. Find the length and breadth of the rectangle.
Question 9 :
State whether the statement is TRUE or FALSE : Two numbers differ by 40, when each number is increased by 8, the bigger becomes thrice the lesser number. If one number is x, then the other number is (40 – x).
Question 10 :
Fifteen added to thrice a whole number gives 93. The number is
Question 11 :
Distance between two stations A and B is 690 km. Two cars start simultaneously from A and B towards each other, and the distance between them after 6 hours is 30 km. If the speed of one car is less than the other by 10 km/hr, find the speed of each car.
Question 13 :
State whether the statement is TRUE or FALSE : In a linear equation, the highest power of the variable appearing in the equation is one.
Question 14 :
State whether the statement is TRUE or FALSE : Sum of the ages of Anju and her mother is 65 years. If Anju’s present age is y years then her mother’s age before 5 years is (60 – y) years.
Question 15 :
Anima left one-half of her property to her daughter, one-third to her son and donated the rest to an educational institute. If the donation was worth Rs. 1,00,000, how much money did Anima have?
Question 17 :
State whether the statement is TRUE or FALSE : The number of boys and girls in a class are in the ratio 5:4. If the number of boys is 9 more than the number of girls, then number of boys is 9.
Question 18 :
After 18 years, Swarnim will be 4 times as old as he is now. His present age is
Question 19 :
If $\frac{5x}{3}-4=\frac{2x}{5}$, then the numerical value of 2x – 7 is
Question 20 :
The sum of two consecutive multiples of 10 is 210. The smaller multiple is
Question 21 :
Solve 4t – 3 – (3t +1) = 5t – 4.
Question 23 :
State whether the statement is TRUE or FALSE : 3 years ago, the age of a boy was y years. His age 2 years ago was (y – 2) years.
Question 24 :
A family spent Rs. 52.00 for circus tickets. This cost included a Rs. 3.25 service fee for the order, with the cost of the circus tickets being Rs. 9.75 each. How many tickets did the family buy?
Question 25 :
A linear equation may have linear expressions on_______of the equality sign.
Question 27 :
Kusum buys some chocolates at the rate of Rs. 10 per chocolate. She also buys an equal number of candies at the rate of Rs. 5 per candy. She makes a 20% profit on chocolates and 8% profit on candies. At the end of the day, all chocolates and candies are sold out and her profit is Rs. 240. Find the number of chocolates purchased.
Question 29 :
A steamer goes downstream from one point to another in 7 hours. It covers the same distance upstream in 8 hours. If the speed of stream be 2 km/hr, find the distance between the ports.
Question 32 :
If 3x – 4 (64 – x) = 10, then the value of x is
Question 34 :
State whether the statement is TRUE or FALSE : An algebraic equation is an equality involving variables.
Question 36 :
The value of x for which the expressions 3x – 4 and 2x + 1 become equal is
Question 37 :
Kaustubh had 60 flowers. He offered some flowers in a temple and found that the ratio of the number of remaining flowers to that of flowers in the beginning is 3:5. Find the number of flowers offered by him in the temple.
Question 38 :
In a two digit number, digit in units place is twice the digit in tens place. If 27 is added to it, digits are reversed. Find the number.
Question 39 :
On subtracting 8 from x, the result is 2. The value of x is
Question 40 :
The solution of the equation 3x – 4 = 1 – 2x is
Question 41 :
State whether the statement is TRUE or FALSE : If a statement is a proportion, the cross-products of the terms are equal.
Question 44 :
Anushka and Aarushi are friends. They have equal amount of money in their pockets. Anushka gave $\frac{1}{3}$ of her money to Aarushi as her birthday gift. Then Aarushi gave a party at a restaurant and cleared the bill by paying half of the total money with her. If the remaining money in Aarushi’s pocket is Rs.1600, find the sum gifted by Anushka.
Question 45 :
A carpenter charged Rs. 2500 for making a bed. The cost of materials used is Rs. 1100 and the labour charges are Rs. 200/hr. For how many hours did the carpenter work?
Question 46 :
State whether the statement is TRUE or FALSE : Two different equations can never have the same answer.
Question 47 :
State whether the statement is TRUE or FALSE : In an equation, variables can be transposed from one side of the equation to the other.
Question 48 :
The present age of father is four times the age of his son. After 10 years, age of father will become three times the age of his son. Find their present ages.
Question 49 :
A steamer goes downstream and covers the distance between two ports in 3 hours. It covers the same distance in 5 hours when it goes upstream. If the stream flows at 3 km/hr, then find what is the speed of the steamer upstream?
