Question

What number must be added to 2, 4, 6,
10 so that the resulting numbers are in
proportion? (Madhyamik. 1997)​

Answer 1

Step-by-step explanation:

Given :-

2, 4, 6, 10

To find :-

What number must be added to 2, 4, 6,

10 so that the resulting numbers are in

proportion?

Solution :-

Given numbers are 2,4,6,10

Let the number should be added to them = X

Then the numbers will be

(2+X),(4+X),(6+X),(10+X)

Product of extremes = (2+X)×(10+X)

=> 2(10+X)+X(10+X)

=> 20+2X+10X+X²

=> X²+12X+20

Product of means = (4+X)×(6+X)

=> 4(6+X)+X(6+X)

=> 24+4X+6X+X²

=> X²+10X+24

We know that

If they are in proportion then

The product of extremes = Product of means

=> X²+12X+20 = X²+10X+24

=> X²+12X+20-X²-10X-24 = 0

=> (X²-X²)+(12X-10X)+(20-24) = 0

=> 0+2X+(-4) = 0

=> 2X-4 = 0

=> 2X = 4

=> X = 4/2

=> X = 2

Therefore,X = 2

Answer:-

The required number should be added to the given numbers is 2

Check:-

If X = 2 then the given numbers will be

(2+2),(4+2),(6+2),(10+2)

=> 4,6,8,12

The product of extremes

= 4×12

= 48

Product of means

= 6×8

= 48

The product of extremes = Product of means

So ,They are in the Proportion.

Used formulae:-

In Proportion,

• The product of extremes = Product of means

Points to know :-

• Equality of ratios is called Proportion.

• The symbol for Proportion is :: (is as)

• If a,b,c,d are in proportion then a:b::c:d => bc = ad.