ratio and proportion sums

8/18/2019 Ratio and Proportion Sums

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A and B together have Rs. 1210. If of A's amount is equal to of B's amount, how much amount does B have?

A. Rs. !0 B. Rs. "

C. Rs. ##0 D. Rs. !!

$wo num%ers are res&ectivel 20( and #0( more than a third num%er. $he ratio of the two num%ers is)

A. 2 ) # B. * ) #

C. ) # D. ! ) +

A sum of mone is to %e distri%uted among A, B, , - in the &ro&ortion of # ) 2 ) ) *. If gets Rs. 1000 more than -

what is B's share?

A. Rs. #00 B. Rs. 1#00

C. Rs. 2000 D. one of these

/eats for athematics, hsics and Biolog in a school are in the ratio # ) + ) ". $here is a &ro&osal to increase these s% 0(, #0( and +#( res&ectivel. hat will %e the ratio of increased seats?

A. 2 ) * ) B. ! ) + ) "

C. ! ) " ) 3 D. one of these

In a mi4ture !0 litres, the ratio of mil5 and water 2 ) 1. If the this ratio is to %e 1 ) 2, then the quanit of water to %e

further added is)

A. 20 litres B. *0 litres

C. 0 litres D. !0 litres

$he ratio of the num%er of %os and girls in a college is + ) ". If the &ercentage increase in the num%er of %os and girl

20( and 10( res&ectivel, what will %e the new ratio?

A. " ) 3 B. 1+ ) 1"

C. 21 ) 22 D. annot %e determined

/alaries of Ravi and /umit are in the ratio 2 ) *. If the salar of each is increased % Rs. 000, the new ratio %ecomes

#+. hat is /umit's salar?

A. Rs. 1+,000 B. Rs. 20,000

C. Rs. 2#,#00 D. Rs. *",000

If 0.+# ) x )) # ) ", then x is equal to)

A. 1.12 B. 1.2

C. 1.2# D. 1.*0



$he sum of three num%ers is 3". If the ratio of the first to second is 2 )* and that of the second to the third is # ) ", th

the second num%er is)

A. 20 B. *0

C. " D. #"

0.

If Rs. +"2 %e divided into three &arts, &ro&ortional to ) ) , then the first &art is)

A. Rs. 1"2 B. Rs. 130

C. Rs. 13! D. Rs. 20

1. $he salaries A, B, are in the ratio 2 ) * ) #. If the increments of 1#(, 10( and 20( are allowed res&ectivel in their

salaries, then what will %e new ratio of their salaries?

A. * ) * ) 10 B. 10 ) 11 ) 20

C. 2* ) ** ) !0 D. annot %e determined

2. If 0( of a num%er is equal to two6third of another num%er, what is the ratio of first num%er to the second num%er?

A. 2 ) # B. * ) +

C. # ) * D. + ) *

*. $he fourth &ro&ortional to #, ", 1# is)

A. 1" B. 2

C. 13 D. 20

. $wo num%er are in the ratio * ) #. If 3 is su%tracted from each, the new num%ers are in the ratio 12 ) 2*. $he smaller

num%er is)

A. 2+ B. **

C. 3 D. ##

#. In a %ag, there are coins of 2# &, 10 & and # & in the ratio of 1 ) 2 ) *. If there is Rs. *0 in all, how man # & coins are

there?

A. #0 B. 100

C. 1#0 D. 200

1. Ratio:



$he ratio of two quantities a and b in the same units, is the fraction and we write it as a ) b.

In the ratio a ) b, we call a as the first term or antecedent and %, the second term or consequent.

7g. $he ratio # ) 3 re&resents#

with antecedent 8 #, consequent 8 3.3

Rule: $he multi&lication or division of each term of a ratio % the same non69ero num%er does not affect the ratio.

7g. ) # 8 " ) 10 8 12 ) 1#. Also, ) ! 8 2 ) *.

2. Proportion:

$he equalit of two ratios is called &ro&ortion.

If a ) b 8 c ) d , we write a ) b :: c ) d and we sa that a, b, c, d are in &ro&ortion.

:ere a and d are called extremes, while b and c are called mean terms.

roduct of means 8 roduct of e4tremes.

$hus, a ) b :: c ) d ;b 4 c < 8 ;a 4 d <.

3. Fourth Proportional:

If a ) b 8 c ) d , then d is called the fourth &ro&ortional to a, b, c .

Third Proportional:

a ) b 8 c ) d , then c is called the third &ro&ortion to a and b.

ean Proportional:

ean &ro&ortional %etween a and b is ab.

Comparison o! Ratios: e sa that ;a ) b< = ;c ) d <a

=c .

b d ". Compounded Ratio:#. $he com&ounded ratio of the ratios) ;a ) b<, ;c ) d <, ;e ) f < is ;ace ) bdf <.

$. Duplicate Ratios:

-u&licate ratio of ;a ) b< is ;a2 ) b2<.

/u%6du&licate ratio of ;a ) b< is ;a ) b<.

$ri&licate ratio of ;a ) b< is ;a* ) b*<.

/u%6tri&licate ratio of ;a ) b< is ;a1>* ) b1>*<.

If a 8 c , then

a b 8

c d . @com&onendo and dividendo

b d a 6 b c 6 d %. &ariations: e sa that x is directl &ro&ortional to y , if x 8 ky for some constant k and we write, x y .

e sa that x is inversel &ro&ortional to y , if xy 8 5 for some constant k and we write, x 1.

y

ratio and proportion sums

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