Question
The difference between the squares of two consecutive numbers is $31$. Find the numbers.
✓
Answer
Let the requierd number $= x$
Then Four-fifth of the number $= x + 1$
$\therefore$ According to the condition:
$(x + 1)^2- (x)^2= 31$
$\Rightarrow x^2+ 2x + 1 - x^2= 31$
$\Rightarrow 2x = 31 - 1 = 3030$
$\Rightarrow\text{x}=\frac{30}{2}=15$
$\therefore$ First number $= 15$
And second number $= 15 + 1 = 16$
Hence numbers are $15, 16$
Check: $(16)^2- (15)^2= 256 - 225 = 31$
Which is given
$\therefore$ Our answer is correct.
Then Four-fifth of the number $= x + 1$
$\therefore$ According to the condition:
$(x + 1)^2- (x)^2= 31$
$\Rightarrow x^2+ 2x + 1 - x^2= 31$
$\Rightarrow 2x = 31 - 1 = 3030$
$\Rightarrow\text{x}=\frac{30}{2}=15$
$\therefore$ First number $= 15$
And second number $= 15 + 1 = 16$
Hence numbers are $15, 16$
Check: $(16)^2- (15)^2= 256 - 225 = 31$
Which is given
$\therefore$ Our answer is correct.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Let us draw some human figures. Measure your friend’s body—the lengths of their head, torso, arms, and legs. Write the ratios as mentioned below -
Perform the following divisions.
(i) $\left(3 p q r-6 p^2 q^2 r^2\right)÷ 3 p q$
(ii) $\left(a x^3-b x^2+c x\right)÷ (-d x)$
(iii) $\left(x^3 y^3+x^2 y^3-x y^4 + x y\right)÷x y$
(iv) $(-q r x y+p r y z-n y z)÷ (-x y z)$
→(i) $\left(3 p q r-6 p^2 q^2 r^2\right)÷ 3 p q$
(ii) $\left(a x^3-b x^2+c x\right)÷ (-d x)$
(iii) $\left(x^3 y^3+x^2 y^3-x y^4 + x y\right)÷x y$
(iv) $(-q r x y+p r y z-n y z)÷ (-x y z)$
Simplify: $\frac{1}{-12}+\frac{2}{-15}$
→Harpreet borrowed $Rs. 20000$ from her friend at $12\%$ per annum simple interest. She lent it to Alam at the same rate but compounded annually. Find her gain after $2$ years.
→ $(\text{x}+2)(\text{x}+3)+(\text{x}-3)(\text{x}-2)-2\text{x}(\text{x}+1)=0$
→Construct a quadrilateral $ABCD$, in which $AB = BC = 3\ cm, AD = 5\ cm,$ $\angle\text{A}=90^\circ$ and $\angle\text{B}=105^\circ.$
→Verify commutativty of addition of rational numbers for the following pairs of rotional number:
$\frac{-11}{5}$ and $\frac{4}{7}$
→$\frac{-11}{5}$ and $\frac{4}{7}$
All the angles of a quadrilateral are equal to each other. Find the measure of each. Is the quadrilateral a parallelogram? What special type of parallelogram is it?
Draw a rhombus whose side is $7.2\ cm$ and one angle is $60^\circ .$
→A rectangular sheet of paper $30\ cm \times 18\ cm$ can be transformed into the curved surface of a right circular cylinder in two ways i.e., either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus formed.
→