31. In an examination, the success to failure ratio was 5 : 2, if the number of failures been 14 more, then the success to failure ratio would have been 9 : 5. The total number of candidates, who appeared for the examination, was:
एक परीक्षा में, सफलता का विफलता से अनुपात 5 : 2 था, यदि विफलताओं की संख्या 14 अधिक होती, तो सफलता का विफलता से अनुपात 9 : 5 होता। परीक्षा में उपस्थित होने वाले छात्रों की कुल संख्या कितनी थी:
Option”B” is correct.
The success to failure ratio = 5 : 2
When the number of failures are 14 more, then the success to failure ratio would have been 9 : 5
Calculation:
Let the successful candidates be 5x and the failure candidates be 2x.
According to Question,
(5x – 14)/(2x + 14) = 9/5
⇒ 25x – 70 = 18x + 126
⇒ x = 196/7 = 28
Total number of candidates who appeared for the examination = 5x + 2x = 7x = 7 × 28 = 196
32. A businessman spends a part of his yearly income and saves a part of it. The ratio of his expenditure to his saving is 5 ∶ 3. If his monthly income is Rs. 40000, what is the amount of his yearly savings? (in Rs.)
एक व्यवसायी अपनी वार्षिक आय का एक हिस्सा व्यय करता है और एक हिस्सा बचत करता है। उसके व्यय का बचत से अनुपात 5 ∶ 3 है। यदि उसकी मासिक आय 40000 रुपये है, तो उसकी वार्षिक बचत की धनराशि क्या है? (रूपए में)
Option”D” is correct
Required saving = 3/8 × 40000 × 12 = Rs. 180000
Detailed solution∶
Given:
The ratio of expenditure and saving = 5 : 3
Monthly income = 40000
Formula used:
if the ratio of savings and expenditure is a : b then yearly saving = [a/(a + b)] × yearly income.
Calculation:
Yearly saving = (3/8) × 40000 × 12
⇒ Yearly saving = 3 × 5000 × 12
⇒ Yearly saving = 180000
∴ Yearly savings is Rs. 180000
33. If Rs.11800 is divided among three friends A, B and C in such a way that 2A = 5B = 7C then find the share of A.
यदि 11800 रुपये तीन दोस्त A, B और C के बीच इस तरह से विभाजित किये जाते है कि 2A = 5B = 7C है, तो ज्ञात कीजिए कि A का हिस्सा कितना होगा?
Option”B” is correct
Given that,
If Rs.11800 is divided among three friends A, B and C in such a way
that 2A = 5B = 7C
Let, 2A = 5B = 7C = LCM of (2, 5, 7)
⇒ 2A = 5B = 7C = 70
There shares will be in the ratio
⇒ A : B : C = 35 : 14 :10
⇒ 35 + 14 + 10 = 59 units
59 units = 11800
1 unit = 200
∴ A’s share will be 35 × 200 = 7000
34. If 4A = 6B = 5C; then find the value of A : B : C. यदि 4A = 6B = 5C है; तो A : B : C का मान ज्ञात कीजिए।
Option”B” is correct
Let 4A = 6B = 5C = K
⇒ 4A = K, 6B = K and 5C = K
⇒ A = K/4, B = K/6 and C = K/5
Now, A : B : C = K/4 : K/6 : K/5
Since, LCM of 4, 6 and 5 = 60
⇒ Multiply (60/K) in each term of the above ratio
⇒ A : B : C = (K/4 × 60/k) : (K/6 × 60/k) : (K/5 × 60/k)
∴ A : B : C = 15 : 10 : 12
35. If U + V = 80 and U : V = 5 : 3, then what is the value of U – V?
यदि U + V = 80 और U : V = 5 : 3 है, तो U – V का मान क्या है?
Option”D” is correct
Let the value of U and V be 5x and 3x
⇒ Given, U + V = 80
⇒ 5x + 3x = 80
⇒ 8x = 80
⇒ x = 10
⇒ U – V = 5x – 3x = 2x = 20
∴ The value of U – V is 20.
36. The ratio of monthly income of Ram and Rahim is 4 : 3 and the ratio of their monthly expenditures is 3 : 2. If each saves Rs. 5000 per month, then what are the respective monthly incomes of Ram and Rahim?
राम और रहीम के मासिक आय का अनुपात 4 : 3 है और उनके मासिक व्यय का अनुपात 3 : 2 है। यदि उनमें से प्रत्येक हर महीने 5000 रुपए की बचत करता है, तो राम और रहीम की मासिक आय क्रमशः क्या है?
Option”B” is correct
The ratio of monthly income of Ram and Rahim is 4 : 3 and the ratio of their monthly expenditures is 3 : 2.
Calculation:
Let the monthly income of Ram and Rahim be 4x and 3x
And their expenditures be 3y : 2y
Income – expenditure = saving
⇒ 4x – 3y = 5000 —- (1)
⇒ 3x – 2y = 5000 —- (2)
Now multiply equation (1) by and (2) by 3
⇒ – x = – 5000
⇒ x = 5000
⇒ Monthly income of Ram = 4x = Rs. 20000
⇒ Monthly income of Rahim = 3x = Rs. 15000
∴ Monthly income of Ram and Rahim are Rs. 20000 and Rs. 15000.
37. A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B’s share?
Option”C” is correct
Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x – 3x = 1000
x = 1000.
B’s share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.
38. An amount is divided between Ram and Rahim in the ratio of 3 : 2 If Ram’s share is Rs. 36000, then what is the total amount?
किसी राशि को राम और रहीम के बीच 3 : 2 के अनुपात में विभाजित किया जाता है। यदि राम का हिस्सा 36000 रु. है, तो कुल राशि क्या है?
Option”A” is correct
Let the amount of Ram and Rahim be 3x and 2x
⇒ Given, 3x = 36000
⇒ 2x = 24000
⇒ The total amount of Ram and Rahim = 3x + 2x = 36000 + 24000 = 60000
∴ The total amount of Ram and Rahim is Rs. 60,000
39. If a sum of Rs. 1,180 is to be divided among A, B and C, such that 2 times A’s share, 5 times B’s share and 7 times C’s share, are equal, then A’s share is:
यदि 1,180 रुपए की एक राशि को A, B और C के बीच इस प्रकार विभाजित किया जाना है जिससे A के हिस्से का दोगुना, B के हिस्से का 5 गुना और C के हिस्से का 7 गुना बराबर हो, तो A का हिस्सा कितना है?
Option”B” is correct
According to the question
2A = 5B = 7C
Let
2A = 5B = 7C = k
2A = k
⇒ A = k/2
5B = k
⇒ B = k/5
7C = k
⇒ C = k/7
Ratio of A, B and C = k/2 : k/5 : k/7 = 70/2 : 70/5 : 70/7 = 35 : 14 : 10
35 + 14 + 10 = 59 unit
59 unit = 1180
⇒ 1 unit = 20
∴ 35 unit = 35 × 20 = 700
Short Trick:
If 2A = 5B = 7C, then
Ratio of A : B : C = 1/2 : 1/5 : 1/7 = 35 : 14 : 10
35 + 14 + 10 = 59 unit
⇒ 59 unit = 1180
⇒ 1 unit = 20
∴ 35 unit = 35 × 20 = 700
40. Find the fraction which bears the same ratio to 1/27 that 3/7 does to 5/9.
उस गुणनखंड को ज्ञात कीजिये जिसका 1/27 के साथ वैसा ही अनुपात है जैसा 3/7 का 5/9 के साथ है।
Option”B” is correct
Let the fraction be x, then according to the question
x = 1000.
B’s share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.
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