CAT QA LINEAR EQUATION QUESTIONS

When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima's age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become

A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is

A donation box can receive only cheques of ₹100, ₹250, and ₹500. On one good day, the donation box was found to contain exactly 100 cheques amounting to a total sum of ₹15250. Then, the maximum possible number of cheques of ₹500 that the donation box may have contained, is

Let k be a constant. The equations kx + y = 3 and 4x + ky = 4 have a unique solution if and only if

The number of pairs of integers(x,y) satisfying x ≥ y ≥ -20 and 2x + 5y = 99 is

Aron bought some pencils and sharpeners. Spending the same amount of money as Aron, Aditya bought twice as many pencils and 10 less sharpeners. If the cost of one sharpener is 2 more than the cost of a pencil, then the minimum possible number of pencils bought by Aron and Aditya together is

Aadi,Bantu,Chintak and Dhoplu have some coins. Aadi says to Bantu "If I give you 8 coins, you will have as many as Chintak has and I shall have 3 less than what Chintak has. But if I take 6 coins from Chintal, I shall have twice as many as Dhaplu has". If Bantu and Dhaplu together have 50 coins, how many cards have Aadi got?

The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157 : 3, then the sum of the two numbers is

When Sunil will be as old as his father is at present, Sunil will be five times as old as his son is atpresent. Also, by then Sunil’s son will be six years older than the age of Sunil at present. The sum of the ages of Sunil’s father and Sunil is 85 years at present. What is the sum of the ages of Sunil’s son and Sunil at present?

Find the minimum value of f(x).

A candle with length 15 cm burns at the rate of 1cm in 1 hr, whereas second candle with 20 cm length burns at the rate of 7 cm in 3 hrs. If the first candle was lit 2 hours before the 2^nd one, what part of each candle was burnt already

before both candles became of equal length?

2x+ 2y+ 7z 14. How many whole number solutions are possible?

If 86 is divided into 4 parts such that twice the first, 5 more than second, 1 less than third and one fifth the fourth are equal. What is the

difference between the fourth and the third part?

For what value of k the equations 2kx + y = 4 and 9x + 0.5ky = 2 have a unique solution where k is a even prime number.

How many solutions exist to the equation 4x2 + 7y = 151 such that both x and y are positive integers?

Given that E = x – y – z + v – w. The variables x, y, z, v and w are assigned distinct values from 0, 5, 7, 8 and 11 (in no particular order). In how many ways can the values be assigned to the variables such that E is always greater than 5?

For the equation 11x + 3y = 273, where x and y are whole numbers. How many pairs of x and y exist such that x*y>0?

When Sunil will be as old as his father is at present, Sunil will be five times as old as his son is at present. Also, by then Sunil’s son will be six years older than the age of Sunil at present. The sum of the ages of Sunil’s father and Sunil is 85 years at present. What is the sum of the ages of Sunil’s son and Sunil at present?

Aadi,Bantu,Chintak and Dhoplu have some coins. Aadi says to Bantu "If I give you 8 coins, you will have as many as Chintak has and I shall have 3 less than what Chintak has. But if I take 6 coins from Chintal, I shall have twice as many as Dhaplu has". If Bantu and Dhaplu together have 50 coins, how many cards have Aadi got?

A candle with length 15 cm burns at the rate of 1cm in 1 hr, whereas second candle with 20 cm length burns at the rate of 7 cm in 3 hrs. If the first candle was lit 2 hours before the 2^nd one, what part of each candle was burnt already before both candles became of equal length?

2x+ 2y+ 7z 14. How many whole number solutions are possible?

If 86 is divided into 4 parts such that twice the first, 5 more than second, 1 less than third and one fifth the fourth are equal. What is the

difference between the fourth and the third part?

For what value of k the equations 2kx + y = 4 and 9x + 0.5ky = 2 have a unique solution where k is a even prime number.

Given that E = x – y – z + v – w. The variables x, y, z, v and w are assigned distinct values from 0, 5, 7, 8 and 11 (in no particular order). In how many ways can the values be assigned to the variables such that E is always greater than 5?