Ratio, Proportion
- A person gave 2/5 part of his income to his elder son and 30 % part to his younger son. He saved his remaining money in three trusts. A, B and C in the ratio of 3 : 5 : 2. If difference between the amount got by his both sons is &8377; 2000, How much amount he saved in trust C ?
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Let the person have ₹ N
Then shares of elder don = ₹ 2N/5
and share of younger son = ₹ 3N/10
According to the question,
2N/5 - 3N/10 = 2000
⇒ N/10 = 2000
⇒ N = 20000
Remaining amount saved in trusts
= 1 - (2N/5 + 3N/10 ) = 1 - (4N + 3N)/10
= 1 - 7N/10 = 3N/10 x 20000 = 6000
given that A : B : C = 3 : 5: 2
∴ Share of C = [2/(3 + 5 +2)] x 6000Correct Option: C
Let the person have ₹ N
Then shares of elder don = ₹ 2N/5
and share of younger son = ₹ 3N/10
According to the question,
2N/5 - 3N/10 = 2000
⇒ N/10 = 2000
⇒ N = 20000
Remaining amount saved in trusts
= 1 - (2N/5 + 3N/10 ) = 1 - (4N + 3N)/10
= 1 - 7N/10 = 3N/10 x 20000 = 6000
given that A : B : C = 3 : 5: 2
∴ Share of C = [2/(3 + 5 +2)] x 6000
= (2/10) x 6000 = ₹ 1200
- A cat takes 5 leaps for every 4 leaps of a a dog but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speeds of the cat to that of the dog ?
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4 leaps of cat = 3 leaps of dog
⇒ 1 leap of cat = 3/4 leap dog
Cat takes 5 leaps for every 4 leaps of dog
∴ Required ratio = (5 x Cat's leap ) : ( 4 x Dog's leap)Correct Option: D
4 leaps of cat = 3 leaps of dog
⇒ 1 leap of cat = 3/4 leap dog
Cat takes 5 leaps for every 4 leaps of dog
∴ Required ratio = (5 x Cat's leap ) : ( 4 x Dog's leap)
= (5 x 3/4 dog's leap) : (4 x Dog's leap)
= 15 : 16
- The respective ratio of Sita's Riya's and Kunal's monthly incomes is 84 : 76 : 89. If riya's annual income ₹ 456000, then what is the sum of Sita and Kunal's annual incomes ? (In some cases monthly income and in some cases annual income is used). ?
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Let monthly income of Sita Riya and Kunal be 84k, 76k and 89k, respectively.
Given annual income of Riya = 456000
∴ Monthly income of Riya = 456000/12 = 38000
∴ 76k = 38000 ⇒ k = 500
So, the monthly income of Sita and Kunal = 84k + 89k = 173k
= 173 x 500 = 86500Correct Option: D
Let monthly income of Sita Riya and Kunal be 84k, 76k and 89k, respectively.
Given annual income of Riya = 456000
∴ Monthly income of Riya = 456000/12 = 38000
∴ 76k = 38000 ⇒ k = 500
So, the monthly income of Sita and Kunal = 84k + 89k = 173k
= 173 x 500 = 86500
Therefore, annual income = 86500 x 12 = ₹ 1038000
- ₹ 2186 are distributed among A, B and C . If money given to them is decreased by ₹ 26, ₹ 28 and ₹ 32 respectively, then they have money in the ratio of 9 :13 : 8. What is the amount given to A?
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Amount given to A= 9k + 26
Amount given to B = 13k + 28
and amount given to C = 8k + 32
According to the question,
(9k + 26) + (13k + 28) + (8k + 32) = 2186Correct Option: C
Amount given to A= 9k + 26
Amount given to B = 13k + 28
and amount given to C = 8k + 32
According to the question,
(9k + 26) + (13k + 28) + (8k + 32) = 2186
⇒ 30 k + 86 = 2186
⇒ 30 k = 2100
∴ k = 70
Hence, amount given to A = 9k + 26 = 9 x 70 + 26
= 630 + 26 = ₹ 656
- In the month of January, Arun's income and expenses were ₹ 15000 and ₹ 9000, respectively. His monthly expenses vary directly as the square of his monthly income. What is his income when it just equals his expenses ?
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According to the question
Expenses ∞ (income)2
⇒ 9000 = K (15000 )2
∴ K = 9000/(15000)2
= 1/25000
Again E = K x 12
⇒ 1 = K x 12 [∴ exenses = income]Correct Option: D
According to the question
Expenses ∞ (income)2
⇒ 9000 = K (15000 )2
∴ K = 9000/(15000)2
= 1/25000
Again E = K x 12
⇒ 1 = K x 12 [∴ exenses = income]
∴ 1 = 1/K = 25000
∴ Required answer = ₹ 25000
