Question

Three numbers are a, b and c are in the ratio 1:2:3 and their average is 600. if a is increased by 10% and b is decreased by 20%, then to get the average increased by 5% , c will be increased by

a. none

b. 150

c. 90

d.100

e.180

Answer 1

Let the three numbers be x,2x,and 3x.

Given that their average is 600.

= > (x + 2x + 3x)/3 = 600

= > 6x = 1800

= > x = 1800/6

= > x = 300.

So,

A = 300

B = 2x = 600

C = 3x = 900

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= > Given that A is increased by 10%.

Value of A = (110/100) * 300 = 330.

= > Given that B is decreased by 8%

Value of B = (80/100) * 600 = 480.

= > Given that the Average is increased by 5%.

So, the new average = (105/100) * 600 = 630.

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Now,

Let x = Increase in c.

= > (330 + 480 + x/3) = 630

= > 330 + 480 + x = 1890

= > 810 + x = 1890

= > x = 1080.

Therefore, the value of c is increased by 1080 - 900 = 180.

Therefore, the answer is Option (E).

Hope it helps!

Answer 2

уσυя αиѕωєя !!

ᴛʜʀᴇᴇ ɴᴜᴍʙᴇʀs ɪɴ ʀᴀᴛɪᴏ = 1:2:3

ʟᴇᴛ ᴛʜᴇ ᴄᴏᴍᴍᴏɴ ʀᴀᴛɪᴏ = x

ᴀ = 1x

ʙ = 2x

ᴄ = 3x

ᴀᴠᴇʀᴀɢᴇ ᴏғ ᴀ, ʙ ᴀɴᴅ ᴄ = 600

sᴏ,

$= > \frac{1x + 2x + 3x}{3} = 600 \\ \\ = > \frac{6x}{3} = 600 \\ \\ = > 2x = 600 \\ \\ = > x = \frac{600}{2} \\ \\ = > x = 300$

ᴀ = 1x = 1 × 300 = 300

ʙ = 2x = 2 × 300 = 600

ᴄ = 3x = 3 × 300 = 900
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$= > a = 300 \times \frac{10}{100} +( 300)\\ \\ = > a = 30 + 300\\ \\ = > a = 330$
___________

$= > b =( 600 )- 600 \times \frac{20}{100} \\ \\ = > b = 600 - 120 \\ \\ = > b = 480$
____________


ᴛʜᴇ ᴀᴠᴇʀᴀɢᴇ ᴡᴀs ɪɴᴄʀᴇᴀsᴇᴅ ʙʏ 5%

sᴏ,

$= > \frac{5}{100} \times 600 + (600) \\ \\ = > 30 + 600 \\ \\ = > 630$


ɴᴇᴡ ᴀᴠᴇʀᴀɢᴇ = 630

ᴄ ᴡɪʟʟ ʙᴇ ɪɴᴄʀᴇᴀsᴇᴅ ʙʏ:

$= > \frac{330 + 480 + c}{3} = 630 \\ \\ cross \: multiplication \\ \\ = > 810 + c = 630 \times 3 \\ \\ = > 810 + c = 1890 \\ \\ = > c = 1890 - 810 \\ \\ = > c = 1080$

ᴄ ᴡɪʟʟ ʙᴇ ɪɴᴄʀᴇᴀsᴇᴅ ʙʏ = 1080 - 900 = 180

ʜᴇɴᴄᴇ, ᴇ. ᴏᴘᴛɪᴏɴ ɪs ᴄᴏʀʀᴇᴄᴛ.

тнαикѕ !!