Correct option is D)

Given, A=B+40%of B

⇒A= 140/100 × B

⇒A/B = 14/10 .....(1)

Also given, B=C−20% of C

⇒B= 80/100 ×C

⇒ B/C = 8/10 ....(2)

So,A/C = A/B × B/C = 14×8 / 10×10 = 28/25

....From (1) and (2)

Therefore, the ratio of A:C is 28:25.

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Verified answer

Gɪᴠᴇɴ :-

A exceeds B by 40% and B is less than C by 20%.

Tᴏ Fɪɴᴅ :-

A:C.

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[tex]\begin{gathered} \\ \huge{ \underbrace{ \underline{ \mathrm{ \: ʀᴇQᴜɪʀᴇᴅ \: ᴀɴsᴡᴇʀ :-}}}} \\ \\ \end{gathered}[/tex]

First understand what is given in the Question :-

• A = B + 40% of B ; and,

• A = [tex] \frac{40}{100}[/tex] B

[tex]\large{\frak{Now,}} [/tex]

[tex]\large \: : \: \longmapsto \: \sf \: { \frac{A}{B} = \frac{14}{10} }[/tex]

[tex]\large \: : \: \longmapsto \: \sf \:{B = C - \frac{20}{100} × C}[/tex]

[tex] \large \: : \: \longmapsto \: \sf \: {{B} = \frac{80}{100} \times C}[/tex]

[tex]\large \: : \: \longmapsto \: \sf \: {\frac{B}{C} = \frac{8}{10} }[/tex]

[tex]\large \: : \: \longmapsto \: \sf \: { \frac{A}{C} = ( \frac{A}{B}) \times ( \frac{B}{C})}[/tex]

[tex]\large \: : \: \longmapsto \: \sf \: { \frac{A}{C} = ( \frac{14 \times 8}{10 \times 10})}[/tex]

[tex]\large \: : \: \longmapsto \: \sf \: { \frac{A}{C} = \frac{28}{25} }[/tex]

[tex] \star \: \large{ \underline{ \boxed{\leadsto{ \red{ \pmb{ \: \frak{A:C = 28 : 25}}}}}}}[/tex]

[tex]{\therefore \:}[/tex] The value of A:C is 28:25.

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