Box Reasoning questions with answers for competitive exams

Most important Box Reasoning questions with answers which includes circle problems, box problems, circle problems, triangles problems for competitive exams like SSC CGL ,SSC CHSL ,CPO ,Bank exams and RRB NTPC etc have been explained in this post. 

Ten Important Box Reasoning questions with answers for competitive exams

Problem #1 

This reasoning problem consists of three figures and every figure have three numbers associated to it . So the solution of this problem is to find the value of question mark using other two numbers associated to it . 

But the main problem is how to utilised these two numbers to get the value of this question mark?

          Now watch carefully the 1st two figures . since these figures have some values at bottom lines. 

          Now we have to find or search the  formula for these two numbers in each figure to utilised them in any possible way to get   number in bottom line. 

         The same formula will be applicable to third figure to find out the value of question mark.

Formula :- 

The difference of  squares of  greater number to smaller number in upper line in every figure is equal to number in lower line in every figure.

4³  - 6² = 64 - 36 = 28 (1st figure)

3³ - 2² = 27 - 4 = 23 ( 2nd figure)

5³  - 5² = 125 - 25 = 100 (3rd figure), This number will be the value of question mark.

Option (3)100  is correct option

Problem #2

This reasoning problem also consists of three figures and every figure have three numbers associated to it . So the solution of this problem is to find the value of question mark using other two numbers associated to it . 

But the main purpose is how to utilised other two numbers to get the value of this question mark?

          Now watch carefully the 1st two figures . since these figures have some values at bottom lines. 

          Now we have to find or search the  formula for these two numbers in each figure to utilised them in any possible way to get   number in bottom line. 

         The same formula will be applicable to third figure to find out the value of question mark.

Formula :- 

The sum of cubes of  1st number and  squares  of  2nd number in upper line in every figure is equal to number in lower row in every figure.

4³ + 6² = 64 + 36 = 100 (1st figure)

2³ + 7² = 8 + 49 = 57 (2nd figure)

4³ + 4² = 64 + 16 = 80 (3rd figure)

Option (4)80  is correct option

Problem #3 

This reasoning problem is a box problem of 3 rows and 3 columns, where the the value of question mark in last row we have to find. 

Formula :- 

Four times the difference of the 1st columns and 2nd column = Number in 3rd  column.

C3 = 4  ×  (C1 - C2)

4 × ( 9 - 4 ) = 4 × 5 = 20 ( Number in 1st row 3rd column ) . 

 

4 × ( 8 - 5 ) = 4 × 4 = 16 ( Number in 2nd row 3rd column ) 

4 × ( 7 - 6 ) = 4 × 1 = 2 ( Number in 1st row 3rd column ) . 

Option (A)2 is correct option

Problem #4

This reasoning problem is a box problem of 4 rows and 3 columns, And we have to find the the value of question mark in 3rd column of 3rd row .

Formula :-  

In every column the sum of 1st and 3rd row is equal to sum of 2nd and 4th row.

i.e.  R1 + R3 = R2 + R4

1st Column 

9 + 7 = 5 + 11 = 12 ( Equal sum in 1st column of R1 & R3 and R2 &R4 ) 

2nd Column 

6 + 4 = 8 + 2 = 10 ( Equal sum in 2nd column of R1 & R3 and R2 &R4 )

3rd Column 

8 + ? = 4 + 7 = 11 ( Equal sum in 3rd column of R1 & R3 and R2 &R4 ) 

 

Hence  8 + ?  = 11

? = 11 - 8 

? = 3 

Option (D)3 is correct option 

Problem #5

This reasoning problem is a box problem of 4 rows and 3 columns, And we have to find the the value of question mark in 3rd column of 2nd row .

Formula :- 

Divide 1st row with the difference of 4th and 3rd row to get the value of 2nd row.

 

R1  ÷ ( R4 - R3 ) = R2

1st Column 

25 ÷ ( 20 - 15 ) = 25  ÷ 5 = 5 ( Number in 2nd row 1st  column ) 

2nd Column 

49 ÷ ( 20 - 13 ) = 49 ÷ 7 = 7 ( Number in 2nd row 2nd  column ) 

3rd Column 

81 ÷ ( 20 - 11 ) = 81 ÷ 9 = 5 = ?  ( Number in 2nd row 3rd column ) 

Option (B)9 is correct option

Problem #6

This reasoning problem is a box problem of 4 rows and 3 columns, And we have to find the the value of question mark in 2nd column of 2nd row .

Formula :-  

Add square root of 1st three row to get the value of number in fourth row. 

R1  +  R2 + R3  = R4

1st Column 

√169 + √64 + √81 = 13 + 8 + 9 = 30 ( Number in 4th row of 1st column ) 

3rd Column 

√1296 + √576 + √100 = 36 + 24 + 10 = 70  ( Number in 4th row of 3rd column ) 

2nd Column 

√625 +  √? + √49 = 25 + √? + 7 =  50 

32 + √? = 50

 √? = 50 - 32

 √? = 18 , Squaring both sides

 ? = 324 ( Number in 4th row of 2nd column ) 

Option (A)324  is correct option

Problem #7

This reasoning problem is also a box problem of 3 rows and 3 columns, And we have to find the the value of question mark in 3rd column of 2nd row .

Formula :- 

Divide the  sum of square of 1st  row to 3rd row to get the value of number in 2nd row. 

(R1²  +  R3 ) ÷  2  =  R2.

1st Column 

( 4² + 4 ) ÷ 2 = ( 16 + 4 ) ÷ 2 = 20 ÷ 2 = 10 ( Number in 2nd row of 1st column ) 

2nd Column 

( 18² + 6 ) ÷ 2 = ( 324 + 6 ) ÷ 2 = 330 ÷ 2 =  165 ( Number in 2nd row of  2nd column ) 

3rd Column 

( 23² + 1 ) ÷ 2 = ( 529 + 1 ) ÷ 2 = 530 ÷ 2 = 265 ( Number in 2nd row of 3rd column ) 

Option (B)265  is correct option

Problem #8 

This reasoning problem is a box problem of 4 rows and 3 columns, And we have to find the the value of question mark in 2nd column of 2nd row .

Formula :-  

Add square root of 1st three row to get the value of number in fourth row. 

R1  +  R2 + R3  = R4.

1st column

2² + 20 = 4 + 20 = 24

2nd column

3² + 30 = 9 + 30 = 39

3rd column

4² + 40 = 16 + 40 = 56

Option (D)56 is correct option

Problem #9

In this reasoning problem two clues are given to find the value of question mark. In 1st clue two numbers 27 and 4 (both are on left hand side ) are associated to give result 139(the number of the right hand side) by using any mathematical operations or combination of mathematical operations. And  in 2nd clue two numbers 31 and 9 are associated to give result 319 by using any mathematical operations or combination of mathematical operations. Similarly we have to associate 21 and 6 by using same mathematical operation to find the value of question mark.

Formula :-  

(1st number  × 2nd number ) + (1st number  + 2nd number ) = Number of right hand side  

(27 × 4 ) + (27 + 4 ) = 108 + 31 = 139.

(31 × 9 ) + (31 + 9 ) = 

279 + 40  = 319.

(21 × 6 ) + (21 + 6 ) = 126 + 27 = 153 = The value of Question mark. 

Option (1)153 is correct option

Problem #10

In this reasoning problem two clues are given to find the value of question mark. In 1st clue two numbers 27 and 4 (both are on left hand side ) are associated to give result 77(the number of the right hand side) by using any mathematical operations or combination of mathematical operations. And  in 2nd clue two numbers 31 and 9 are associated to give result 239 by using any mathematical operations or combination of mathematical operations. Similarly we have to associate 21 and 6 by using same mathematical operation to find the value of question mark.

Formula :- 

 (1st number  × 2nd number ) - (1st number + 2nd number )  = Number of right hand side 

(27 × 4 ) - (27 + 4 ) = 108 - 31 = 77.

(31 × 9 ) - (31 + 9 ) = 

279 - 40 = 239.

(21 × 6 ) - (21 + 6 ) = 126 - 27 = 99 = The value of Question mark. 

Option (2)99 is correct option

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