Question

1. Sum of two numbers is 20 and their difference is 4. Which is the greater
of the two numbers.
A) 16
B) 14
C) 12.
D) 8
​

Answer 1

✯ Given :-

• Sum of two numbers = 20
• Difference between the numbers = 4

✯ We need to find :-

• Greater number = ?

✯ Solution :-

Let the number be ‘x’

Now , the two number‘s :-

◎ x , x + 4

Now , by the given information ,

⇒ x + ( x + 4 ) = 20

Simplifying ,

⇒ x + x + 4 = 20

⇒ 2x + 4 = 20

⇒ 2x = 20 - 4

⇒ 2x = 16

⇒ x = 16 ÷ 2

⇒ x = 8

Now , finding both the numbers,

◉ x = 8

◉ x + 4 = 8 + 4 = 12

∴ 12 > 8

Hence , greater number is 12. So , option C is your answer .

Answer 2

$\sf{\bold{\purple{\star{\underline{\underline{Given}}}}}}$

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• Sum of 2 numbers is 20

⠀⠀⠀⠀

• Difference of 2 numbers is 4

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$\sf{\bold{\purple{\star{\underline{\underline{To\: Find}}}}}}$

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• Greater number = ??

⠀⠀⠀⠀

$\sf{\bold{\purple{\star{\underline{\underline{Solution}}}}}}$

⠀⠀⠀⠀

• let 2 numbers be x and y

⠀⠀⠀⠀

Acc. to 1st given statement :-

⠀⠀⠀⠀

x + y = 20 ---- ( i )

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Acc. to 2nd given statment :-

⠀⠀⠀⠀

x - y = 4 ---- ( ii )

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• Adding eq ( i ) and ( ii )

⠀⠀⠀⠀

$\sf : \implies\:{\frak{ x + y + x - y = 20 + 4 }}$

⠀⠀⠀⠀

$\sf : \implies\:{\frak{ x + x = 20 + 4}}$

⠀⠀

$\sf : \implies\:{\frak{ 2x = 24 }}$

⠀⠀⠀⠀

$\sf : \implies\:{\frak{ x = \dfrac{24}{2} }}$

⠀⠀⠀

$\sf : \implies\:{\frak{ x = 12 }}$

⠀⠀⠀⠀

$\sf{\star{\boxed{\orange{\frak{ x = 12 }}}}}$

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• Putting value of y in eq ( ii )

⠀⠀⠀⠀

$\sf : \implies\:{\frak{ 12 - y = 4 }}$

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$\sf : \implies\:{\frak{ y = 12 - 4 }}$

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$\sf : \implies\:{\frak{ y = 8 }}$

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$\sf{\star{\boxed{\orange{\frak{ y = 8 }}}}}$

⠀⠀⠀⠀

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• Two required numbers are 12 and 8 .

⠀⠀⠀⠀

10 > 8

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• Therefore greater number is 12