type 5 shares & partnership based ratio & proportion problems Section-Wise Topic Notes With Detailed Explanation And Example Questions

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The following question based on ratio & proportion topic of quantitative aptitude

Questions : By mistake, instead of dividing 117 among A, B and C in the ratio 1 2 1 3 1 4 : : it was divided in the ratio of 2 : 3 : 4. Who gains the most and by how much?

(a) C, 20

(b) C, 25

(c) B, 3

(d) A, 28

The correct answers to the above question in:

Answer: (b)

Original ratio of A, B and C

= $1/2 : 1/3 : 1/4$ = 6 : 4 : 3

Share of A

= $6/13 × 117$ = Rs.54

Share of B

= $4/13 × 117$ = Rs.36

and share of C

= $3/13 × 117$ = Rs.27

The ratio of A, B and C by mistake = 2 : 3 : 4

Share of A = $2/9 × 117$ = Rs.26

Share of B = $3/9 × 117$ = Rs.39

Share of C = $4/9 × 117$ = Rs.52

Therefore, it is clear from above calculation that C gains maximum i.e. Rs.25.

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Read more shares and partnership based ratio and proportion Based Quantitative Aptitude Questions and Answers

Question : 1

A man divides his property so that his son’s share to his wife’s and wife’s share to his daughter’s are both as in the ratio 3 : 1. If the daughter gets 10,000 less than son, the value (in rupees) of the whole property is

a) 18,250

b) 17,000

c) 16,000

d) 16,250

Answer: (d)

Son : wife = 3 : 1 = 9 : 3

Wife : daughter = 3 : 1

Son : wife : daughter

= 9 : 3 : 1

Sum of ratios = 9 + 3 + 1 = 13

If total wealth be Rs.x, then

Son’s share - daughter’s share

= Rs.10,000

${9x}/13 - x/13$ = 10,000

${9x - x}/13$ = 10,000

8x = 13,00,00

$x = {13,00,00}/8$ = Rs.16250

Question : 2

An amount of money is to be distributed among P, Q and R in the ratio of 2 : 7 : 9. The total of P’s and Q’s share is equal to R’s share. What is the difference between the shares of P and Q ?

a) 9000

b) Information inadequate

c) 7500

d) 5000

Answer: (b)

Let the amount to be distributed be Rs.x.

P : Q : R = 2 : 7 : 9

Sum of the ratios = 2+7 + 9 = 18

P = $2/18 × x = x/9$

Q = $7/18$ x

R = ${9x}/18 = x/2$

As given,

$x/9 + {7x}/18 = x/2$

Thus, we get no conclusion.

Amount should necessarily be known.

Question : 3

Divide 1250 among A, B, C, so that A gets 2 9 of B’s share and C gets 3 4 of A’s share.

a) 150, 800, 300

b) 200, 900, 75

c) 200, 900, 150

d) 200, 800, 250

Answer: (c)

A = B × $2/9 = {2B}/9$

$C= {3A}/4 ; A = 4/3C$

Ratio of A : B : C = 4 : 18 : 3

Share of A = $4/25 × 1250$ = Rs.200

Share of B = $18/25 × 1250$ = Rs.900

Share of C = $3/25 × 1250$ = Rs.150

Question : 4

3400 is divided among A, B, C, D in such a way that the share of A and B, B and C, C and D may be as 2 : 3, 4 : 3 and 2 : 3 respectively. The sum of shares of B and D is

a) 2000

b) 1720

c) 1680

d) 2040

Answer: (d)

A:B=2:3
B:C=4:3
C:D=2:3

A : B : C : D = 2 × 4 × 2 : 3 × 4 × 2 : 3 × 3 × 2 : 3 × 3 × 3

or, A : B : C : D = 16 : 24 : 18 : 27

Sum of the ratios

= 16 + 24 + 18 + 27 = 85

B’s share

= Rs.$24/85 × 3400$ = Rs.960

D’s share

= Rs.$27/85 × 3400$ = Rs.1080

The required sum

= Rs.(1080 + 960) = Rs.2040

Question : 5

A sum of 76 is divided among A, B and C in such a way that A gets 7 more than that what B gets and B gets 6 more than what C gets. The ratio of their shares is

a) 32 : 24 : 20

b) 19 : 25 : 33

c) 32 : 25 : 19

d) 19 : 24 : 33

Answer: (c)

B’s share = Rs.b

A’s share = Rs.(b + 7)

C’s Share = Rs.(b - 6)

b + b + 7 + b - 6 = 76

3b = 76 - 1 = 75

b = Rs.25

A’s share = 25 + 7 = Rs.32

C’s share = 25 - 6 = Rs.19

Required ratio = 32 : 25 : 19

Question : 6

If 126.50 is divided among A, B and C in the ratio of 2 : 5 : 4, the share of B exceeds that of A by

a) 34.50

b) 33.50

c) 35.50

d) 36.50

Answer: (a)

A : B : C = 2 : 5 : 4

Sum of ratios = 2 + 5 + 4 = 11

Difference

= $(5/11 - 2/11) × 126.50$

= $3/11 × 126.50$ = Rs.34.50

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