Question

Sum of two numbers is 35 and their difference is 13, then the numbers are:-
(a) 24, 12
(b) 24, 11
(c) 12, 11
(d) none​

Answer 1

Gɪᴠᴇɴ :-

• Sum of Two Nos. = 35 .
• Difference of Them = 13.

Tᴏ Fɪɴᴅ :-

• Find the two Numbers ?

Sᴏʟᴜᴛɪᴏɴ :-

Let us assume That, two given numbers are x & y..( where x > y. )

Than,

sum of them is given as 35 .

So,

→ x + y = 35 --------------- Eqn(1) .

and,

Difference of them is given as 13,

So,

→ x - y = 13 --------------- Eqn(2) .

Now adding Both Eqns . we get,

→ (x + y) + (x - y) = 35 + 13

→ x + x + y - y = 48

→ 2x = 48

→ x = 24 (Ans.)

Putting This value in Eqn(1) , we get,

→ 24 + y = 35

→ y = 35 - 24

→ y = 11 (Ans.)

Hence, value of x & y is 24 & 11 . (Option B).

Answer 2

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

• Sum of two numbers=35
• difference of two numbers=13

${\bf{\blue{\underline{Find:}}}}$

• Two numbers=?

${\bf{\blue{\underline{Now:}}}}$

Let us suppose that the two numbers are a and b,

☞ Sum of two numbers = 35

→ A+B =35.....(1)

☞ difference of two numbers =13

→ A-B =13.......(2)

${\bf{\blue{\underline{by \: substitution \: method \: :}}}}$

From(1)

${\implies{\sf{ \: A = 35 - B....(3)}}}$

Now,put the value of A in (2)

${\implies{\sf{ \: (35 - B ) - B = 13}}}$

${\implies{\sf{ \: 35 -2B = 13}}}$

${\implies{\sf{ \: -2B = 13 - 35}}}$

${\implies{\sf{ \: -2B = - 22}}}$

${\implies{\sf{ \: B = \frac{22}{2} }}}$

${\implies \boxed{\sf{ B = 11 }}}$

Now put the value of B in (3),

${\implies {\sf{ A = 35 - (11) }}}$

${\implies \boxed {\sf{A=2 4}}}$

$\boxed {\sf{\purple{ Hence \: the \: two \: numbers \: are \: 24 ,\: 11}}}$

$\bigstar \: \boxed {\sf{\purple{ \: Option \:(b) \: is \: Correct}}}$