Chapter 3 - Moderate Questions

A lady has only 25-paisa and 50-paisa coins in her purse. If she has 100 coins in all totalling Rs. 39, how many coins of each kind she has?

Find two numbers such that the sum of twice the first and thrice the second is 92, and four times the first exceeds seven times the second by 2.

Find two numbers such that the sum of thrice the first and the second is 142, and four times the first exceeds the second by 138.

If 45 is subtracted from twice the greater of two numbers, it results in the other number. If 21 is subtracted from twice the smaller number, it results in the greater number. Find the numbers.

If 2 is added to each of two given numbers, their ratio becomes 1 : 2. However, if 4 is subtracted from each of the given numbers, the ratio becomes 5 : 11. Find the numbers.

The sum of the digits of a two-digit number is 12. The number obtained by interchanging its digits exceeds the given number by 18. Find the number.

A number consisting of two digits is seven times the sum of its digits. When 27 is subtracted from the number, the digits are reversed. Find the number.

The sum of digits of a two digit number is 15. The number obtained by reversing the order of digits of the given number exceeds the given number by 9. Find the given number.

A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.

A two-digit number is such that the product of its digits is 35. If 18 is added to the number, the digits interchange their places. Find the number.

A two digit number is such that the product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.

The sum of a two digit number and the number obtained by reversing the order of its digits is 121, and the two digits differ by 3. Find the number.

If 2 is added to the numerator of a fraction, it reduces to 1/2 and if 1 is subtracted from the denominator, it reduces to 1/3. Find the fraction.

In a given fraction, if 1 subtracted from the numberator and 2 is added to the denominator, it becomes 1/2. If 7 is subtracted from the numerator and 2 is subtracted from the denominator, it becomes 1/3. The fraction is

The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3, they are in the ratio 2 : 3. Determine the fraction.

There are two examination rooms A and B. If 10 candidates are sent from A and B, the number of students in each room is same. If 20 candidates are sent from B to A, the number of students in A is double the number of students in B. Find the number of students in each room.

A man invested an amount at 10% per annum and another amount at 8% per annum simple interest. Thus, he received ₹ 1350 as annual interest. Had he interchanged the amounts invested, he would have received ₹ 45 less as interest. What amounts did he invest at different rates ?

A man sold a chair and a table together for Rs.1,520 thereby making a profit of 25% on the chair and 10% on the table. By selling them together for Rs. 1535 he could have made a profit of 10% on the chair and 25% on the table. Find the cost price of each.

Points A and B are 70 km. apart on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 7 hours, but if they travel towards each other, they meet in one hour. Find the speed of the two cars.

Abdul traveled 300 km by train and 200 km by taxi, it took him 5 hours 30 minutes. But if he travel 260 km by train and 240 km by bus he takes 6 minutes longer. Find the speed of the train and of the taxi.

Places A and B are 160 km apart on a highway. One car starts from A and another from B at the same time. If they travel in the same direction, they meet in 8 hours. But, if they travel towards each other, they meet in 2 hours. Find the speed of each car.

A sailor goes 8 km downstream in 40 minutes and returns in 1 hours. Determine the speed of the sailor in still water and the speed of the current.

The length of a room exceeds its breadth by 3 meters. If the length is increased 3 meters and the breadth is decreased by 2 meters, the area remains the same. Find the length and the breadth of the room.

The area of a rectangle gets reduced by 67 square meters, when its length is increased by 3 m and breadth is decred by 4 m. If the length is reduced by 1 m breadth is increased by 4 m, the area is increased by 89 square meters. Find the dimesions of the rectangle.

Five years hence, fathers age will be three times the age of his son. Five years ago, father was seven times as old as his son. Find their present ages.

Two years ago, a father was five times as old as his son. Two years later, his age will be 8 more than three times the age of the son. Find the present ages of father and son.

If twice the sons age in years is added to the fathers age, the sum is 70. But if twice the fathers age is added to the sons age, the sum is 95. Find the ages of father and son.

The present age of a woman is 3 years more than three times the age of her daughter. Three years hence, the woman's age will be 10 years more than twice the age of her daughter. Find their present ages.

90% and 97% pure acid solutions are mixed to obtain 21 litres of 95% pure acid solution. Find the quantity of each type of acids to be mixed to from the mixture.

In a ABC, ∠A = x°, ∠B = (3x − 2)°, ∠C = y°. Also, ∠C − ∠B = 9° . Find the three angles.