A, B and C are three positive numbers such that the average of three-fifth of A and 30 \% of B is 13.5, and the average of \frac{3}{8} times of B and 25 \% of C is 15 . If A is equal to \frac{5}{12} times of C, then the sum of all three numbers A, B and C is

SSC CHSL 11 Aug 2021 Shift 2 Paper

Section: Quantitative Aptitude

Question : 64 of 100

Marks: +1, -0

A, B

and

C

are three positive numbers such that the average of three-fifth of

A

and

30 \%

B

13.5

, and the average of

\frac{3}{8}

times of

B

and

25 \%

C

15 .

A

is equal to

\frac{5}{12}

times of

C

, then the sum of all three numbers

A, B

and

C

Solution:

According to the question,

A=\;{5}/{12} \;\text " of "\; C

. . . (i)

\;{\;{3}/{5} A+30 \% \;\text " of "\; B}/{2} \;\; =13.5

⇒ \;\; 6 A+3 B \;\; =270 \;\; \;\; \;\text ". . . (ii), "\;

\;\text " and "\; \;{\;{3}/{8} B+25 \% \;\text " of "\; C}/{2} \;\; =15

⇒ \;\; 3 B+2 C \;\; =240 \;\; \;\text ". . . (iii) "\;

On solving Eqs.(i), (ii) and (iii),

270-6 × \;{5}/{12} × C=240-2 C

⇒ \;\; \;{5}/{2} C-2 C=270-240

⇒ \;\; C=60

∴ A=25

and

B=40

∴ \;\; A+B+C=25+40+60=125

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