Ratio - Study Mode
[#171] Three numbers are in the ratio 5 : 7 : 12. If the sum of the first and the third is greater than the second by 50. The sum of the three numbers is = ?
Correct Answer
(B) 120
Explanation
Solution: Let the number are 5x, 7x and 12x According to the question, ⇒ 5x + 12x = 7x + 50 ⇒ 17x - 7x = 50 ⇒ 10x = 50 ⇒ x = 5 Sum of all three numbers = 5x + 7x + 12x = 24x = 24 × 5 =120
[#172] The weights of two persons A and B are in the ratio of 3 : 5. A's weight increases by 20% and the total weight of A and B together becomes 80kg, with an increase of 25%. By what percent did the weight of B increase ?
Correct Answer
(C) 28%
Explanation
Solution: Let the initial total weight of A and B be x kg. Then, $$eqalign{
& = 125\% { ext{ of }}x = 80 cr
& Rightarrow x = 80 imes frac{{100}}{{125}} = 64{ ext{kg}} cr
& { ext{A's initial weight}} cr
& = left( {64 imes frac{3}{8}}
ight){ ext{kg}} cr
& = 24{ ext{kg}}{ ext{}} cr
& { ext{B's initial weight}} cr
& = left( {64 imes frac{5}{8}}
ight){ ext{kg}} cr
& = 40{ ext{kg}} cr
& { ext{A's new weight}} cr
& = 120\% { ext{ of }}24{ ext{kg}} cr
& = 28.8{ ext{kg}}{ ext{}} cr
& { ext{B's new weight}} cr
& = left( {80 - 28.8}
ight){ ext{kg}} cr
& = 51.2{ ext{kg}} cr
& { ext{Increase in B's weight}} cr
& = left( {51.2 - 40}
ight){ ext{kg}} cr
& = 11.2{ ext{kg}} cr
& herefore { ext{Increase }}\% cr
& = left( {frac{{11.2}}{{40}} imes 100}
ight)\% cr
& = 28\% cr} $$
[#173] Mrs. Richi Rich inherits 3224 gold coins and divides them amongst her 3 daughters Lalita, Palita and Salita in a certain ratio. Out of the total coins each of them received, Lalita sells her 50 coins, Palita donates 85 of her coins and Salita makes jewellery out of her 39 coins. Now the ratio of gold coins with them is 24 : 21 : 16 respectively. How many coins did Lalita receive from her mother ?
Correct Answer
(D) 1250
Explanation
Solution: Let the number of coins with Lalita, Palita and Salita in the end be 24x, 21x and 16x respectively. Then, Number of coins received by Lalita, Palita and Salita from their mother are (24x + 50), (21x + 85) and (16x + 39) respectively So, (24x + 50) + (21x + 85) + (16x + 39) = 3224 ⇒ 61x = 3050 ⇒ x = 50 Hence, number of coins received by Lalita from her mother = (24 × 50 + 50) = 1250
[#174] Railway fares of 1st, 2nd and 3rd classes between two stations were in the ratio of 8 : 6 : 3. The fares of 1st and 2nd class were subsequently reduced by $$frac{1}{6}$$ and $$frac{1}{12}$$ respectively. If during a year the ratio between the passengers of 1st, 2nd and 3rd classes was 9 : 12 : 26 and the total amount collected by the sale of tickets was Rs. 1088, then find the collection from the passengers of 1st class.
Correct Answer
(D) Rs. 320
Explanation
Solution: Let the initial fares of 1st, 2nd and 3rd class be Rs. 8x, Rs. 6x, and Rs. 3x respectively $$eqalign{
& { ext{Revised fare of 1st class}} cr
& { ext{ = }}frac{5}{6}{ ext{of Rs}}.8x cr
& = { ext{Rs}}.left( {frac{{20x}}{3}}
ight) cr
& { ext{Revised fare of }}2{ ext{nd class}} cr
& { ext{ = }}frac{{11}}{{12}}{ ext{of Rs}}.6x cr
& = { ext{Rs}}{ ext{.}}left( {frac{{11x}}{2}}
ight) cr} $$ Let the number of passengers of 1st, 2nd and 3rd class be 9y, 12y and 26y respectively Then, $$eqalign{
& = frac{{20x}}{3} imes 9y + frac{{11x}}{2} imes 12y + 3x imes 26y = 1088 cr
& Rightarrow 60xy + 66xy + 78xy = 1088 cr
& Rightarrow 204xy = 1088 cr
& Rightarrow xy = frac{{1088}}{{204}} = frac{{16}}{3} cr} $$ ∴ Collection from passengers of 1st class = 60xy $$eqalign{
& = { ext{Rs}}{ ext{.}}left( {60 imes frac{{16}}{3}}
ight) cr
& = { ext{Rs}}.320 cr} $$
[#175] If 5 person together can make 5 mats in 5 hours, then 10 person in 10 hours will make = ?
Correct Answer
(A) 20 mats
Explanation
Solution: $$eqalign{
& frac{{{m_1} imes {h_1}}}{{{w_1}}} = frac{{{m_2} imes {h_2}}}{{{w_2}}} cr
& Rightarrow frac{{5 imes 5}}{5} = frac{{10 imes 10}}{{{w_2}}} cr
& Rightarrow {w_2} = 20 cr} $$