Problems on Numbers Questions

If the numerator of a fraction is increased by $\frac{1}{4}$ and the denominator is decreased by $\frac{1}{3}$, the new fraction obtained is $\frac{33}{64}$. What was the original fraction?

When the numerator of a fraction increases by 4, the fraction increases by $\frac{2}{3}$. The denominator of the fraction is

A fraction is such that if the double of the numerator and the triple of the denominator is changed by $+10$ percent and $-30$ percent respectively, then we get 11 percent of $\frac{16}{21}$. Find the fraction.

Of the three numbers, the sum of the first two is 73; the sum of the second and the third is 77 and the sum of the third and thrice the first is 104. The third number is

The sum of the squares of two positive integers is 100 and the difference of their squares is 28. The sum of the numbers is

Directions : Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. What is the value of the two-digit number $ab$? I. The difference between its digits is 2. II. The sum of its digits is 4.

Directions : Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. How much is four-fifths of the number? I. Three-fourths of the number is 2.5 less than its four-fifths. II. Half of the number added to it is 75.

Directions : Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. What is the difference between the digits of a two-digit number? I. The sum of the digits of that number is 8. II. One-fifth of that number is 15 less than half of 44.

Directions : Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. What is the value of the two-digit number? I. The product of the digits is 72 and the difference between the digits is 1. II. The digit at the unit place is greater than the other.

Directions: Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the given question. What will be the sum of two numbers? I. Among the two numbers, the bigger number is greater than the smaller number by 6. II. 40% of the smaller number is equal to 30% of the bigger number. III. The ratio between half of the bigger number and one-third of the smaller number is 2 : 1.

Directions: Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the given question. What is the two-digit number? I. Digit in the ten's place is four times the digit in the unit's place. II. The two digits are not equal. III. Digit in the ten's place is cube of the digit in unit's place.

4/7th of the boys and 6/11th of girls of a school participated in marathon. If the number of participating students is 208 out of which 124 are boys, what is the total, number of students in the school? [NICL—AAO Exam, 2015]