PAN BALANCE PROBLEMS WITH SHAPES

Problem 1 :

Work out the value of the diamond in each question. Notice the same symbol is added 3 items. Your 3 times tables will help here.

Solution :

By observing the picture, three diamonds is equal to 12.

4 + 4 + 4 = 12

So, the value of one diamond = 4

Problem 2 :

Solution :

By observing the picture, three diamonds is equal to 36.

12 + 12 + 12 = 36

So, the value of one diamond = 12

Problem 3 :

Solution :

By observing the picture, three diamonds is equal to 45.

15 + 15 + 15 = 45

So, the value of one diamond = 15

Find the value of the symbols. Remember that if a symbol is used more than once, it means it is same value again.

Problem 4 :

Solution :

By observing the figure, value of 3 stars is equal to 9.

3 + 3 + 3 = 9

So, the value of one star = 3

Problem 5 :

Solution :

By observing the figure, the product of two hearts is equal to 36. Value of one heart is equal to 6.

6 × 6 = 36

So, the value of one heart = 6

Problem 6 :

Solution :

By observing the figure, the product of two smiles is equal to 49.

7 × 7 = 49

So, the value of one smile = 7

Find the value of the symbols and then check if you are right by using the same value in the equation alongside it.

Problem 7 :

Solution :

Product of two diamonds = 81

9 x 9 = 81

So, the value of one diamond = 9

Next,

Diamond x triangle = 36

9 x ? = 36

9 x 4 = 36

So, the value of one triangle is 4.

Problem 8 :

Solution :

By observing the figure in the left side,

The sum of one circle and two circles is equal to 29

Circle + 2 stars = 29

5 + 24 = 29

5 + 12 + 12 = 29

One circle = 5, one star = 12

Problem 9 :

Look carefully at the example above and follow the steps to find out the values of these secret symbols:

Solution :

One asterisk = 15 (Given)

asterisk + Circle = 45

15 + 1 circle = 45

1 Circle = 45 - 15 ==> 30

1 circle = 30

1 triangle + 1 circle = 65

1 triangle + 30 = 65

1 triangle = 65 - 30

1 triangle = 35

Problem 10 :

Solution :

One diamond = 54 (Given)

One diamond / 1 circle = 9

54/circle = 9

1 circle = 6

1 triangle / 1 circle = 3

1 triangle / 6 = 3

18/6 = 3

1 triangle = 18

This time you must find the value of 3 different symbols using the clues in each step:

Problem 11 :

Solution :

Product of 2 stars = 16

One star = 4

Circle + star = 100

96 + 4 = 100

1 circle = 96

Circle - star = 1 triangle

96 - 4 = 1 triangle 

1 triangle = 92

Problem 12 :

Solution :

Sum of two triangles = 50

25 + 25 = 50

Value of 1 triangle = 25

1 triangle / 1 circle = 5

25 / 1 circle = 5

25/5 = 5

1 circle = 5

1 circle + 1 triangle = 1 star

5 + 25 = 1 star

1 star = 30

Problem 13 :

Solution :

1 star + 1 circle = 20

By observing the second picture, it is very clear 1 star is not  equal to 10.

Let us work from backwards.

13 - 1 star = 5

1 star = 13 - 5

1 star = 8

1 star x 1 triangle = 72

8 x 9 = 72

1 triangle = 9

1 triangle + 1 circle = 20

9 + 1 circle = 20

1 circle = 20 - 9

1 circle = 11