IQ question

The whole circle $\bigcirc = 4$ and the whole square $\square = 8$ . Therefore,

$\large \begin{array} {ccccccccc} \frac 34 \bigcirc & + & \frac 12 \square & = & \frac 34 \times 4 & + & \frac 12 \times 8 &= &7 \\ \frac 12 \bigcirc & + & \frac 34 \square & = & \frac 12 \times 4 &+ & \frac 34 \times 8 & = & 8 \\ \frac 14 \bigcirc & + & 1 \square & = & \frac 14 \times 4 & + & 1 \times 8 & = & 9 \\ 1 \bigcirc & + & 1 \square & = & 1 \times 4 &+ & 1 \times 8 & = & \boxed{12} \end{array}$

Adding 1st and 3rd equation gives

(3/4)circle+(1/2)square+(1/2)circle +(3/4) square=15

Taking circle and square common

(5/4)circle+(5/4)square=15

Circle+square=(15*4)÷5

=12

suppose, circle=C and square=S

now, $\frac{3C}{4}$ $+\frac{2S}{4}$ $=7$ ..........[1st picture from left side,row 1]

or, $3C+2S=28$ .................................(1)

again, $\frac{2C}{4}$ $+\frac{3S}{4}$ $=8$ .........[1st picture from left side row 2]

or, $2C+3S=32$ .................................(2)

now, multiplying equation (2) by 3 and multiplying equation (1) by 2 and doing (2)-(1), we get ,

$\text{6C+9S=96}$

$\text{6C+4S=56}$

$\text{=5S=40}$ or, $S=8$

applying the value into equation(2), we get, C=4

so, $C+S=4+8=12$ ..........[the answer]

Using only two of the given equations:

Add the two columns on the left. We find $1\tfrac14\ \text{circle}\ +\ 1\tfrac14\ \text{square} = 15.$ Multiply by $4/5$ : $\text{circle}\ +\ \text{square} = \frac 45 \times 15 = \boxed{12}.$