Maharashtra Class 9 Answered

Total income of Ramesh,Suresh,preeti is 8,07,000 Rs.The percentage of their expenses are 75%,80%,90% respectively.If the ratio of their savings is 16:17:12,then find annual savings of each of them.

Asked by Jdjayle | 30 Nov, 2018, 06:19: PM

Expert Answer

Let income of Ramesh Rs.x, income of Suresh Rs.y and income of Preeti Rs.z

we have x+y+z = Rs. 8,07,000 ........................(1)

Percentage of Ramesh's expense 75%; savings 25%, hence his savings Rs. (25x/100 )

Percentage of Suresh's expense 80%; savings 20%, hence his savings Rs. (20x/100 )

Percentage of Preeti's expense 90% ; savings 10%, hence her savings Rs. (10x/100 )

begin mathsize 12px style fraction numerator R a m e s h space S a v i n g s over denominator S u r e s h space s a v i n g s end fraction space equals space fraction numerator begin display style bevelled fraction numerator 25 x over denominator 100 end fraction end style over denominator begin display style bevelled fraction numerator 20 y over denominator 100 end fraction end style end fraction space equals space fraction numerator 5 x over denominator 4 y end fraction equals 16 over 17 space space o r space 64 space y space equals space 85 x space semicolon space h e n c e space y space equals 85 over 64 x space end style

.......................(2)

begin mathsize 12px style fraction numerator R a m e s h space S a v i n g s over denominator P r e e t i space s a v i n g s end fraction space equals space fraction numerator begin display style bevelled fraction numerator 25 x over denominator 100 end fraction end style over denominator begin display style bevelled fraction numerator 10 z over denominator 100 end fraction end style end fraction space equals space fraction numerator 5 x over denominator 2 z end fraction equals 16 over 12 space space space space o r space space 32 space z space equals space 60 x space semicolon space h e n c e space z space equals space 15 over 8 x space end style

......................(3)

let us substitute for y and z using eqn.(2) and eqn.(3) in eqn.(1) and solve for x

begin mathsize 12px style x space plus space 85 over 64 x space plus space 15 over 8 x space equals space 807000 64 x space plus space 85 x plus 120 x space equals space 807000 cross times 64 space space o r space 269 x space equals space 807000 cross times 64 space space space o r space x space equals space R s. space factorial comma 92 comma 000 space.............. left parenthesis 4 right parenthesis end style

from eqn.(4) and eqn.(2), we get y as :

begin mathsize 12px style y space equals space 85 over 64 cross times 192000 space equals space R s. space 2 comma 55 comma 000 end style

from eqn.(4) and eqn.(3), we get z as :

begin mathsize 12px style z space equals space 15 over 8 cross times 192000 space equals space R s. space 3 comma 60 comma 000 end style

Ramesh's savings = 192000×(25/100) = Rs.48000

Suresh's savings = 255000×(20/100) = Rs. 51000

Preeti's savings = 360000×(10/100) = Rs. 36000

Answered by Thiyagarajan K | 01 Dec, 2018, 12:03: AM

Maharashtra Class 9 Answered

Concept Videos

Rational Numbers ...

Rational and Irrational Numbers

Remainder Theorem

Factorisation: Factor Theorem

Substitution Method

CALL US / WHATSAPP

Please Login or Sign up to continue!

Maharashtra Class 9 Answered

Concept Videos

Rational Numbers ...

Rational and Irrational Numbers

Remainder Theorem

Factorisation: Factor Theorem

Substitution Method

Choose Filters

Open In Ask A Doubt App ?

Get in Touch

Call / Whats App