problem archive
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Solve $2x + 3y = 11$ and $2x - 4y = -24$ and hence find the value of $m$ for which $y = mx + 3$ -
Form the pair of linear equations for the following problems and find their solution by substitution method. (i) The difference between two numbers is... -
Form the pair of linear equations for the following problems and find their solution by substitution method. (ii) The larger of two supplementary angl... -
Form the pair of linear equations for the following problems and find their solution by substitution method. (iii) The coach of a cricket team buys 7 ... -
Form the pair of linear equations for the following problems and find their solution by substitution method. (iv) The taxi charges in a city consist o... -
Form the pair of linear equations for the following problems and find their solution by substitution method. (v) A fraction becomes $\frac{9}{11}$, if... -
Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob's age was seven times that of his son. What are their pr... -
The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save ₹ 2000 per month, find thei... -
Use elimination method to find all possible solutions of the following pair of linear equations: \(2x + 3y = 8\) \(4x + 6y = 7\) -
The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How man... -
Solve the following pair of linear equations by the elimination method and the substitution method: (i) x + y = 5 and 2x - 3y = 4 (ii) 3x + 4y = 10 an... -
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method: (i) If we add 1 to th... -
Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Meena got 25 notes in all. Find how many notes o... -
A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹ 27 for a book kept for ... -
Suppose a charity trust decides to build a prayer hall having a carpet area of 300 square metres with its length one metre more than twice its breadth... -
John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would l... -
A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of t... -
(i) Let the number of toys produced on that day be x. Therefore, the cost of production (in rupees) of each toy that day = 55 - x So, the total cost o... -
Example 2: Check whether the following are quadratic equations: (i) (x - 2)^2 + 1 = 2x - 3 (ii) x(x + 1) + 8 = (x + 2)(x - 2) (iii) x(2x + 3) = x^2 + ... -
Check whether the following are quadratic equations: (i) \((x+1)^2 = 2(x-3)\) (ii) \(x^2 - 2x = (-2)(3-x)\) (iii) \((x-2)(x+1) = (x-1)(x+3)\) (iv) \((...