Linear Equations & Fraction Word Problems

1️⃣ The sum of a number and 3/5 of it is 64. Find the number.

A) 35 B) 40 C) 45 D) 50


2️⃣ A rope is 5/6 m long; 2/3 m is cut off and the remaining rope is divided into 4 equal parts. Find the length of each part.

A) 1/12 m B) 1/6 m C) 1/8 m D) 1/4 m


3️⃣ Three times a number decreased by 5 gives 31. Find the number.

A) 10 B) 11 C) 12 D) 13


4️⃣ A man spends 2/5 of his income on rent and 1/4 of the remaining on food; if he saves ₹18,000, find his income.

A) ₹40,000 B) ₹45,000 C) ₹48,000 D) ₹50,000


5️⃣ The sum of two consecutive integers is 47. Find the smaller integer.

A) 22 B) 23 C) 24 D) 25


6️⃣ A tank is filled with 7/8 of water; 1/4 of the filled water is used. What fraction of the tank is still filled?

A) 9/16 B) 5/8 C) 11/16 D) 3/4


7️⃣ Five more than twice a number equals three less than four times the number. Find the number.

A) 3 B) 4 C) 5 D) 6


8️⃣ A cyclist covers 3/5 km in 12 minutes; at the same speed, how much distance will he cover in 1 hour?

A) 3 km B) 4 km C) 5 km D) 6 km


9️⃣ A number multiplied by 3/4 and then increased by 6 becomes 21. Find the number.

A) 16 B) 18 C) 20 D) 24


🔟 A box contains 5/6 kg sugar; how many such boxes are needed to make 10 kg sugar?

A) 10 B) 11 C) 12 D) 15


1️⃣1️⃣ The perimeter of a rectangle is 64 m; if length is 4 m more than twice the breadth, find the breadth.

A) 6 m B) 8 m C) 10 m D) 12 m


1️⃣2️⃣ A student spends 1/3 of his money on books and 2/5 of the remaining on stationery; if ₹240 is left, find the total money.

A) ₹600 B) ₹720 C) ₹750 D) ₹800


1️⃣3️⃣ How many pieces of length 3/4 m can be cut from a rope 9 m long?

A) 10 B) 11 C) 12 D) 13


1️⃣4️⃣ The sum of a number and 7/8 of it is 75. Find the number.

A) 40 B) 45 C) 48 D) 50


1️⃣5️⃣ A father is 4 times as old as his son; after 5 years, he will be 3 times as old. Find the son’s present age.

A) 8 years B) 10 years C) 12 years D) 14 years

1️⃣6️⃣ The sum of a number and 2/3 of it is 70. Find the number.

A) 30 B) 36 C) 42 D) 48


1️⃣7️⃣ A rope 7/4 m long has 5/6 m cut off; the remainder is divided equally into 3 parts. Find the length of each part.

A) 7/36 m B) 11/36 m C) 13/36 m D) 5/18 m


1️⃣8️⃣ Four times a number increased by 1/2 of the number gives 54. Find the number.

A) 10 B) 12 C) 14 D) 16


1️⃣9️⃣ A man spends 3/8 of his income on rent and 2/5 of the remaining on food; if he saves ₹18,000, find his income.

A) ₹48,000 B) ₹50,000 C) ₹54,000 D) ₹60,000


2️⃣0️⃣ The sum of three consecutive integers is 99. Find the largest integer.

A) 32 B) 33 C) 34 D) 35


2️⃣1️⃣ A tank is 5/6 full; 1/5 of the filled water is used and then 1/3 of the remaining is again used. What fraction of the tank is left filled?

A) 4/9 B) 5/9 C) 8/15 D) 2/3


2️⃣2️⃣ The length of a rectangle is 3/2 times its breadth; if the perimeter is 70 m, find the breadth.

A) 10 m B) 12 m C) 14 m D) 16 m


2️⃣3️⃣ A cyclist covers 5/6 km in 20 minutes. At the same speed, how far will he travel in 2 hours?

A) 4 km B) 5 km C) 6 km D) 10 km


2️⃣4️⃣ A number when multiplied by 5/6 and then reduced by 7 becomes 13. Find the number.

A) 20 B) 22 C) 24 D) 30


2️⃣5️⃣ How many pieces each of length 7/8 m can be cut from a rope 14 m long?

A) 12 B) 14 C) 16 D) 18


2️⃣6️⃣ The sum of a number and 4/5 of it is 54. Find the number.

A) 20 B) 25 C) 30 D) 35


2️⃣7️⃣ The present age of a father is 5 times the age of his son; after 10 years, the father will be 3 times as old. Find the son’s present age.

A) 8 years B) 10 years C) 12 years D) 14 years


2️⃣8️⃣ A man walks 3/4 km in 15 minutes. At the same speed, how long will he take to walk 5 km?

A) 1 h 30 min B) 1 h 40 min C) 1 h 50 min D) 2 h


2️⃣9️⃣ A number is such that 1/3 of it minus 5 equals 1/6 of it plus 2. Find the number.

A) 36 B) 42 C) 48 D) 54


3️⃣0️⃣ The area of a rectangle is 120 m²; if the length is 5/3 times the breadth, find the breadth.

A) 6 m B) 8 m C) 9 m D) 12 m


3️⃣1️⃣ The sum of a number, 1/2 of it, and 1/3 of it is 66. Find the number.

A) 24 B) 30 C) 36 D) 42


3️⃣2️⃣ A rope 9/2 m long is cut into two parts such that one part is 2/3 of the other. Find the length of the longer part.

A) 9/5 m B) 12/5 m C) 15/5 m D) 18/5 m


3️⃣3️⃣ Three consecutive integers are such that the sum of the first and third is 68. Find the middle integer.

A) 33 B) 34 C) 35 D) 36


3️⃣4️⃣ A man spends 1/4 of his income on house rent, 2/5 of the remaining on food, and 1/3 of the rest on travel. If he saves ₹9,000, find his income.

A) ₹30,000 B) ₹36,000 C) ₹40,000 D) ₹45,000


3️⃣5️⃣ A number when multiplied by 3/5, reduced by 4, and then divided by 2 gives 8. Find the number.

A) 30 B) 40 C) 50 D) 60


3️⃣6️⃣ A tank is 3/4 full; 2/3 of the filled water is used. What fraction of the tank remains filled?

A) 1/6 B) 1/4 C) 3/8 D) 1/2


3️⃣7️⃣ The length of a rectangle is 7/4 times its breadth. If the perimeter is 88 m, find the breadth.

A) 8 m B) 10 m C) 12 m D) 16 m


3️⃣8️⃣ A cyclist covers 7/10 km in 14 minutes. At the same speed, how far will he travel in 2 hours 20 minutes?

A) 6 km B) 7 km C) 8 km D) 9 km


3️⃣9️⃣ The sum of two numbers is 72. One number is 3/5 of the other. Find the smaller number.

A) 27 B) 30 C) 32 D) 36


4️⃣0️⃣ A number when added to 1/4 of itself gives 45. Find the number.

A) 30 B) 36 C) 40 D) 45


4️⃣1️⃣ A rope 10 m long is cut into pieces each of length 5/6 m. How many pieces are obtained?

A) 10 B) 11 C) 12 D) 13


4️⃣2️⃣ The present age of a mother is 3 times the age of her daughter. After 12 years, the sum of their ages will be 72 years. Find the daughter’s present age.

A) 8 years B) 10 years C) 12 years D) 14 years


4️⃣3️⃣ A number is such that 2/5 of it + 7 = 1/2 of it − 3. Find the number.

A) 40 B) 50 C) 60 D) 70


4️⃣4️⃣ The area of a rectangle is 192 m². If the length is 4/3 times the breadth, find the breadth.

A) 8 m B) 10 m C) 12 m D) 16 m


4️⃣5️⃣ A man walks 5/8 km in 10 minutes. How long will he take to walk 6 km at the same speed?

A) 1 h 20 min B) 1 h 30 min C) 1 h 36 min D) 1 h 40 min

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