MAT Mathematical Skills Free Practice Set

1) The difference between the compound interest and the simple interest earned at the end of 3rd year on a sum of money at a rate of 10% per annum is Rs. 77.5. What is the sum?

Rs. 3,500

Rs. 2,500

Rs. 3,000

Rs. 2,000

The difference between the compound interest and the simple interest earned at the end of 3rd year on a sum of money at a rate of 10% per annum is Rs. 77.5. To find the sum, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal sum, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. Let P be the sum we are trying to find. The compound interest earned after 3 years is P(1 + 0.1/1)^(1*3) - P. The simple interest earned after 3 years is P * 0.1 * 3. According to the given information, the difference between these two values is Rs. 77.5. Solving this equation will give us the value of P, which is Rs. 2,500.

Explanation

The difference between the compound interest and the simple interest earned at the end of 3rd year on a sum of money at a rate of 10% per annum is Rs. 77.5. To find the sum, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal sum, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years. Let P be the sum we are trying to find. The compound interest earned after 3 years is P(1 + 0.1/1)^(1*3) - P. The simple interest earned after 3 years is P * 0.1 * 3. According to the given information, the difference between these two values is Rs. 77.5. Solving this equation will give us the value of P, which is Rs. 2,500.

2) Ten years ago, Nidhi's mother Sita was 4 times old than her daughter. After 10 years, the mother will be twice older than the daughter. What is the present age of Sita?

40 years

50 years

30 years

45 years

Ten years ago, Nidhi's mother Sita was 4 times older than her daughter. This means that if we subtract 10 from the present age of Sita, it would be four times the present age of Nidhi. After 10 years, the mother will be twice older than the daughter. This means that if we add 10 to the present age of Sita, it would be twice the present age of Nidhi. By solving these two equations, we can determine that the present age of Sita is 50 years.

Explanation

Ten years ago, Nidhi's mother Sita was 4 times older than her daughter. This means that if we subtract 10 from the present age of Sita, it would be four times the present age of Nidhi. After 10 years, the mother will be twice older than the daughter. This means that if we add 10 to the present age of Sita, it would be twice the present age of Nidhi. By solving these two equations, we can determine that the present age of Sita is 50 years.

3) A medical college having 600 students collected fund to build a laboratory. The amount contributed by each boy and girl was equal to their respective total numbers in the college. The UGC grant was equal to the fund collected by the students. Ratio of boys to girls is 7: 3. What amount of money was available to build the laboratory?

Rs. 2,08,000

Rs. 4,17,600

Rs. 3,52,000

Date inadequate

In this question, we are given that the ratio of boys to girls in the college is 7:3. Let's assume that there are 7x boys and 3x girls in the college. It is also given that the amount contributed by each boy and girl is equal to their respective total numbers in the college. Therefore, each boy contributes 7x and each girl contributes 3x.

The total fund collected by the students is the sum of the contributions of all the boys and girls, which is (7x + 3x) = 10x.

It is also given that the UGC grant is equal to the fund collected by the students. Therefore, the UGC grant is also 10x.

Now, we need to find the value of x. Since the total number of students in the college is 600, we can set up the equation 7x + 3x = 600. Solving this equation, we get x = 60.

Substituting the value of x back into the equation for the UGC grant, we get 10x = 10 * 60 = 600.

Therefore, the amount of money available to build the laboratory is Rs. 4,17,600.

Explanation

In this question, we are given that the ratio of boys to girls in the college is 7:3. Let's assume that there are 7x boys and 3x girls in the college. It is also given that the amount contributed by each boy and girl is equal to their respective total numbers in the college. Therefore, each boy contributes 7x and each girl contributes 3x.

The total fund collected by the students is the sum of the contributions of all the boys and girls, which is (7x + 3x) = 10x.

It is also given that the UGC grant is equal to the fund collected by the students. Therefore, the UGC grant is also 10x.

Now, we need to find the value of x. Since the total number of students in the college is 600, we can set up the equation 7x + 3x = 600. Solving this equation, we get x = 60.

Substituting the value of x back into the equation for the UGC grant, we get 10x = 10 * 60 = 600.

Therefore, the amount of money available to build the laboratory is Rs. 4,17,600.

4) Two taps can fill a tank in 24 min and 36 min respectively. A 3rd outlet pipe can empty the tank in 30 min. If all of them are opened simultaneously, what will be the time required to fill the tank?

1 hour 15 min

20 min

12 min

None of these

The 3rd outlet pipe is emptying the tank while the two taps are filling it. Since the time required to empty the tank is less than the time required to fill it, the tank will never be filled. Therefore, the correct answer is "None of these".

Explanation

The 3rd outlet pipe is emptying the tank while the two taps are filling it. Since the time required to empty the tank is less than the time required to fill it, the tank will never be filled. Therefore, the correct answer is "None of these".

5) In an election of two candidates, the candidate who gets 41% votes is rejected by a majority of 2412 votes. Find the total number of votes polled.

4100

13400

5900

7100

The candidate who gets 41% of the votes is rejected by a majority of 2412 votes. This means that the other candidate received 59% of the votes. To find the total number of votes, we can set up the equation 41% + 59% = 100%. Let x be the total number of votes. So, 41% of x is rejected by a majority of 2412 votes, which means that 59% of x is equal to 2412 votes. Solving this equation, we find that x = 4100, which is the total number of votes polled.

Explanation

The candidate who gets 41% of the votes is rejected by a majority of 2412 votes. This means that the other candidate received 59% of the votes. To find the total number of votes, we can set up the equation 41% + 59% = 100%. Let x be the total number of votes. So, 41% of x is rejected by a majority of 2412 votes, which means that 59% of x is equal to 2412 votes. Solving this equation, we find that x = 4100, which is the total number of votes polled.

MAT MATheMATical Skills Free Practice Set