GRADE 6 MATH WORD PROBLEMS WITH ANSWERS

Problem 1 :

A train travels 18 km/hr. How many meters will it travel in 12 minutes.

(A) 3600         (B) 4200          (C) 5100

Answer :

Speed of the train  =  18 km/hr 

Speed of train in m/sec  =  18 ⋅ (5/18)

  =  5 m/sec

12 minutes  =  12 (60)

=  720 seconds

Distance covered in 720 seconds  =  time taken (Speed)

  =  720(5)

  =  3600 m

So, the distance covered is 3600 m.

Problem 2 :

The average age of 30 kids is 9 years. If the age of teacher is included, the average age becomes 10 years. What is the age of teacher?

(A) 26            (B) 58            (C) 40

Answer :

The average age of 30 kids is 9 years

Let x be the age of teacher 

Average age  =  Sum of ages/Total number of ages

9  =  sum of ages of 30 kids/30

Sum of ages of 30 kids  =  30 ⋅ 9

  =  270

Sum of ages of kids and teacher  =  270 + x

Average age of kids and teacher  =  (270 + x)/31

10  =  (270 + x)/31

10 (31)  =  270 + x

310  =  270 + x

x  =  310 - 270

x  =  40

So, the required age is 40 years.

Problem 3 :

If the height of a cylinder is 7 cm and the radius is 3 cm, then the surface area of the cylinder is ?

(A) 150          (B) 132          (B) 143

Answer :

Height of the cylinder  =  7 cm

Radius of the cylinder  =  3 cm

Curved surface area of cylinder  =  2 Π r h

  =  2 ⋅ (22/7) ⋅ 7 ⋅ 3

  =  2 ⋅ 22 ⋅ 3

  =  44 ⋅ 3

 =  132 cm²

So, the answer is 132 cm²

Problem 4 :

Jack purchases a calculator for $350 and sells for $420.Then the percentage of profit is

(A) 10%           (B) 20%             (C) 50%

Solution :

Cost price of a calculator  =  $350

Selling price of the calculator  =  $420

Profit  =  Selling price - Cost price

  =  420 - 350

  =  70

profit percentage  =  (profit/cost price) ⋅ 100

  =  (70/350) ⋅ 100

  =  (1/5) ⋅ 100

  =  20%

So, the answer is 20%

Problem 5 :

The average of 6 numbers is 8. What is the 7th number, so that its average will become 10 ?

(A) 15        (B) 22        (C) 12

Answer :

The average of 6 numbers is 8

Average  =  Sum of numbers/Number of terms

8  =  Sum of 6 numbers/6

6(8)  =  Sum of 6 numbers

Sum of 6 numbers  =  48

If 7th term is added with this total, its average will become 10

Let x be the 7th term

(48 + x)/7  =  10

48 + x  =  70

x  =  70 - 48

x  =  22  

So, the answer is 22.

Problem 6 :

Find the number of prime factors of 6¹⁰ × 7¹⁷ × 55²⁷

(A) 100            (B) 91          (C) 64

Answer :

  =  6 ¹⁰ × 7 ¹⁷ × 55²⁷

  =  (2 x 3) ¹⁰ × 7 ¹⁷ × (5 x 11)²⁷

  =  2¹⁰ x 3¹⁰ × 7 ¹⁷ × 5²⁷ x 11²⁷

Total number of prime factors  =  10 + 10 + 17 + 27 + 27

  =  91

So, the answer is 91.

Problem 7 :

If 12 man can do a piece of work in 36 days. Within how many days 18 men can do the same work ?

(A) 27        (B) 24          (C) 22

Answer :

Work done  =  Number of days ⋅ number of men

  =  36 ⋅ 12

  =  432  ---(1)

Work done  =  Number of days ⋅ 18  ----(2)

432  =  Number of days ⋅ 18

Number of days  =  432 / 18

Number of days  =  24

So, the required number of days is 24.

Problem 8 :

A man traveled from the village to the post office at the rate of 25 kmph and walked back at the rate of 4 kmph. If the entire journey took 5 hours 48 minutes, determine the distance of the post office from that village.

(A) 20           (B) 13         (C) 20

Answer :

The distance covered in both cases are same.

Time  =  Distance / Speed

T₁  =  Distance / 25

T₂  =  Distance / 4

5 hours 48 minutes  =  5   4/5  hours

29/5  =  (Distance / 25) + (Distance / 4)

29/5  =  (4 Distance + 25 Distance) / 100

  (29/5) ⋅ (100/29)  =  Distance 

  Distance  =  20 km

Problem 9 :

The sum of reciprocal of (3/2) and the reciprocal of 3 is

(A) 2           (B) 1            (C) 5

Answer :

Reciprocal of 3/2 is 2/3

reciprocal of 3 is 1/3

Sum of these two numbers  =  (2/3) + (1/3)

  =  (2 + 1)/3

  =  3/3

  =  1

So, the correct answer for this question is 1

Problem 10 :

It is 9 hours now in a 12 hour clock. What will be the time after 18 hours ?

(A) 2           (B) 4          (C) 3

Answer :

Now, the time is 9 hours. We want to know the time after 18 hours.

To get answer for our question, we have to do the following steps.

Step 1 :

Add 18 to 9

Step 2 :

Divide the result by the divisor 12

Step 3 :

Take the remainder

9 + 18  =  27

When 27 is divided by 12, the remainder is 3

The time after 18 hours will be 3 hours. So the answer is 3 hours.

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