Ratio - Study Mode

[#186] The ratio of the income of A and B in the last year was 4 : 3. The
ratios of their individual incomes in the last year and the present year are 3 : 4 and 5 : 6, respectively. If their total income in the present year in Rs. 24.12 lakhs, then the sum of the income (in Rs. lakh) of A in the last year and that of B in the present year is:
Correct Answer

(C) 20.52

Explanation

Solution: [x08egin{array}{*{20}{c}}
{}&{{ ext{Last year}}}&{{ ext{Current year}}} \
{{ ext{A}} o }&{{3_{ imes 5 imes 4}} = 60}&{{4_{ imes 5 imes 4}} = 80} \
{{ ext{B}} o }&{{5_{ imes 3 imes 3}} = 45}&{{6_{ imes 3 imes 3}} = 54}
end{array}] The ratio of income of A and B in the last year is 4 : 3. So we're making last year's income 60, 45. Present age ratio of both = 80 : 54 Sum of present age of both = 80 + 54 = 134 units 134 units → 24.12 lakh 1 unit → $$frac{{24.12}}{{134}}$$ Sum of income of A in final year and income of B in present year = 60 + 54 = 114 114 units → $$frac{{24.12}}{{134}}$$ × 114 = 20.52 Sum of income of A in final year and income of B in present year = 20.52 lakh Alternate solution [x08egin{array}{*{20}{c}}
{}&{ ext{A}}&{ ext{B}} \
{{ ext{Previous year }} o }&{4x}&{3x}
end{array}] A's present salary : Ratio of final year to present year = 3 : 4 3 units = 4x 4 units $$ = 4x imes frac{4}{3} = frac{{16}}{3}x$$ B's present salary : Final year and present year = 5 : 6 5 units = 3x 6 units $$ = 3x imes frac{6}{5} = frac{{18}}{5}x$$ [x08egin{array}{*{20}{c}}
{}&{{ ext{A}},,,}&{{ ext{B}},,,} \
{{ ext{Present year }} o }&{frac{{16}}{3}x}&{frac{{18}}{5}x}
end{array}] $$eqalign{
& frac{{16}}{3}x + frac{{18}}{5}x = frac{{134}}{{15}}x o 24.12{ ext{ lakh}} cr
& x = frac{{24.12 imes 15}}{{134}} cr} $$ Final year income of A and Present year income of B. $$eqalign{
& = 4x + frac{{18}}{5}x = frac{{38}}{5}x cr
& frac{{38}}{5}x o frac{{24.12 imes 15}}{{134}} imes frac{{38}}{5} = 20.52 cr} $$ Final year income of A and Present year income of B = 20.52 lakh

[#187] A man has in all Rs. 640 in the denominations of one-rupee, five-rupee and ten-rupee notes. The number of each type of notes are equal. What is the total number of notes he has?
Correct Answer

(B) 120

Explanation

Solution: [x08egin{array}{*{20}{c}}
{}&{{ ext{Rs}}{ ext{. 1}}}&:&{{ ext{Rs}}{ ext{. 5}}}&:&{{ ext{Rs}}{ ext{. 10}}}&{} \
{{ ext{Number of notes}}}&1&:&1&:&1&{} \
{}&x&:&x&:&x&{ = x08oxed{3x}{ ext{ number of notes}}} \
{{ ext{So, Value}}}&x&:&{5x}&:&{10x}&{ = x08oxed{16x}{ ext{ value of notes}}}
end{array}] $$eqalign{
& x + 5x + 10x = 640 cr
& 16x = 640 cr
& x08oxed{x = 40} cr
& herefore { ext{Number of notes }}40 imes 3 = 120 cr} $$

[#188] Rs. 3,600 is divided between Seema, Komal and Rita, such that the ratios of the shares of Seema : Komal = 1.5 : 2 and Komal : Rita = 2 : 2.5. Find Rita's share.
Correct Answer

(A) Rs. 1,500

Explanation

Solution: Ratio of shares of Seema and Komal = 1.5x : 2x Ratio of shares of Komal and Rita = 2x : 2.5x Ratio of shares of Seema, Komal and Rita = 1.5x : 2x : 2.5x According to the question 1.5x + 2x + 2.5x = 3600 ⇒ 6x = 3600 ⇒ x = $$frac{{3600}}{6}$$ ⇒ x = 600 ∴ Share of Rita = 2.5 × 600 = Rs. 1,500

[#189] In a factory with 400 employees, the ratio of the number of male employees to that of female employees is 5 : 3. There are 87.5% regular employees in the factory. If 92% of male employees are regular employees, then what is the percentage of regular female employees?
Correct Answer

(A) 80%

Explanation

Solution: [x08egin{array}{*{20}{c}}
{{ ext{Male}}}&{}&{{ ext{Female}}}&{}&{} \
x08egin{gathered}
5 hfill \
,,,,,,,{ downarrow ^{ imes 50}} hfill \
250 hfill \
end{gathered} &x08egin{gathered}
: hfill \
hfill \
hfill \
end{gathered} &x08egin{gathered}
3 hfill \
,,,,,,,{ downarrow ^{ imes 50}} hfill \
150 hfill \
end{gathered} &x08egin{gathered}
o hfill \
hfill \
hfill \
end{gathered} &x08egin{gathered}
8 - 400 hfill \
1 - 50 hfill \
hfill \
end{gathered}
end{array}] Total regular employees = 400 × 87.5% = 400 × $$frac{{875}}{{100 imes 10}}$$ xa0= 350 Regular male employees = 250 × 92% = 250 × $$frac{{92}}{{100}}$$ = 230 ∴ Regular female employees = 350 - 230 = 120 ∴ % of regular female employees = $$frac{{120}}{{150}}$$ × 100% = 80%

[#190] A bag has Rs. 51.25 in the form of 2-rupee, 50-paise and 25-paise coins in the ratio of 3 : 5 : 7. What is the total number of 50-paise coins?
Correct Answer

(C) 25

Explanation

Solution: [x08egin{array}{*{20}{c}}
{}&{{ ext{Rs}}{ ext{. 2}}}&{}&{{ ext{50 Paise }}}&{}&{{ ext{25 Paise}}} \
{{ ext{Coins}}}&3&:&5&:&7
end{array}] Amount = Number of coins × Face value Amount = $$6:frac{5}{2}:frac{7}{4}$$ According to question, $$eqalign{
& Rightarrow 6x + frac{{5x}}{2} + frac{{7x}}{4} = 51.25 cr
& Rightarrow 24x + 10x + 7x = 51.25 imes 4 cr
& Rightarrow 41x = 205 cr
& Rightarrow x = frac{{205}}{{41}} cr
& x08oxed{x = 5} cr} $$ ∴ Total number of 50 paise coins = 5 × 5 = 25