41. If A : B = 3 : 5 and B : C = 2 : 3, then A : B : C is equal to:
यदि A : B = 3 : 5 और B : C = 2 : 3 है, तब A : B : C का मान है:
Option”C” is correct
A : B = 3 : 5 — (1)
B : C = 2 : 3 — (2)
Multiply by 2 in equation (1) and multiply by 5 in equation (2)
A : B : C = 6 : 10 : 15
42. The ratio of salaries to Hamid, Clement and Ganesh is 3 : 5 : 7. If Ganesha gets Rs. 884 more than Hamid, then how much is Clement’s salary (in Rs.)?
हामिद, क्लेमेंट और गणेश के वेतन का अनुपात 3 : 5 : 7. है। यदि गणेश को हामिद से 884 रुपए अधिक मिलते हैं, तो क्लेमेंट का वेतन (रुपए में) कितना है?
Option”B” is correct
Let the salaries of Hameed, Clement and Ganesh be 3x, 5x, and 7x
According to the question
7x – 3x = 884
⇒ 4x = 884
⇒ x = 884/4 = 221
∴ Salary of Clement = 5 × 221 = Rs. 1105
43. A diamond is broken into four parts in the ratio 1 : 2 : 3 : 4. If the price of diamond is in proportion to square of its weight then find the percentage decrease in the price of diamond considering that the price of actual diamond is Rs. 100000.
एक हीरे को 1 : 2 : 3 : 4 के अनुपात में चार भागों में तोड़ दिया जाता है। यदि हीरे का मूल्य उसके वजन के वर्ग के अनुपात में है तो वास्तविक हीरे का मूल्य रू. 100000 मानते हुए हीरे के मूल्य में प्रतिशत हानि ज्ञात कीजिये।
Option”C” is correct
Diamond broken into 4 parts in the ratio 1 : 2 : 3 : 4
Price of actual diamond is Rs. 100000
Concept:
In this type of questions we can calculate the actual weight of diamond by adding all the ratios.
Calculation:
Let the weight of 4 parts be x, 2x, 3x, and 4x
So actual weight of diamond = x + 2x + 3x + 4x = 10x
According to question
The price of diamond is in proportion to square of its weight
100x2 = 100000
⇒ x2 = 1000
So the price of diamond after it is broken = x2 + 4x2 + 9x2 + 16x2 = 30x2 = Rs. 30000
So decrease in price = 100000 – 30000 = 70000
∴ Percentage decrease in price = 70%
44. The salaries of Charan and Rajat are in the ratio of 5: 4. If the salary of each increases by Rs. 3,000, then the new ratio becomes 6: 5. What is Charan’s initial salary?
चरण और रजत का वेतन 5 : 4 के अनुपात में है। यदि प्रत्येक के वेतन में 3,000 रुपये की वृद्धि होती है, तो नया अनुपात 6 : 5 हो जाता है। चरन का प्रारंभिक वेतन क्या है?
Option”B” is correct
Ratio of salary of charan and rajat = 5: 4
Each salary is increased by Rs. 3000
New ratio = 6 : 5
Calculation:
Let the salary of charan and rajat = 5x and 4x
Each salary is increased by Rs. 3000
According to question:
⇒ (5x + 3000)/(4x + 3000) = 6: 5
⇒ 25x + 15000 = 24x + 18000
⇒ x = 3000
∴ Charan initial salary = 5 × 3000 = Rs. 15000
45. The ratio of male and female members of a club is 5 ∶ 6. The ratio will be reversed if 22 female members leave the club. The number of male members is
एक क्लब के पुरुष और महिला सदस्यों का अनुपात 5 ∶ 6 है। 22 महिला सदस्यों के क्लब छोड़ने पर यह अनुपात उलट जाता है। पुरुष सदस्यों की संख्या है
Option”C” is correct
Ratio of male and female members of a club = 5 ∶ 6
After 22 female left, New ratio = 6 ∶ 5
Calculation:
Let the number of male be 5x and female be 6x
Number of female left = 22
According to question,
5x/(6x — 22) = 6/5
⇒ 36x = 25x + 132
⇒ 11x = 132 or x = 12
Male members = 5x = 60
46.If p : q = 6 : 5 and q : r = 4 : 3, then (q + r)/p is equal to
यदि p : q = 6 : 5 और q : r = 4 : 3 है, तो (q + r)/p बराबर है:
Option”C” is correct
Given:
Ratio of p : q and q : r = 6 : 5 and 4 : 3
Calculation:
p : q = 6 : 5 —- (1) × 4
q : r = 4 : 3 —- (2) × 5
Multiply by 4 in equation (1) and multiply by 5 in equation (2), we get
p : q : r = 24 : 20 : 15
⇒ (q + r)/p
⇒ (20 + 15)/24
⇒ 35/24
47.If a : b : c = 1 : 3 : 5 and 6a – 2b + 3c = 90 then value of b = ?
यदि a : b : c = 1 : 3 : 5 और 6a – 2b + 3c = 90 तो b का मान है = ?
Option”A” is correct
Given: a : b : c = 1 : 3 : 5
Concept used: Let a = k, b = 3k, c = 5k
Calculation: Here a : b : c = k : 3k : 5k
⇒ Putting the values in the given equation 6a – 2b + 3c
⇒ we get, 6k – 6k + 15k = 90
⇒ 15k = 90
∴ k = 6 and b = 6 × 3 = 18
48. If a : b = 3 : 5, b : c = 4 : 3 and c : d = 2 : 5 then find a : b : c : d.
अगर a : b = 3 : 5, b : c = 4 : 3 और c : d = 2 : 5 तो ज्ञात कीजिए a : b : c : d.
Option”C” is correct
a : b = 3 : 5, b : c = 4 : 3 and c : d = 2 : 5
Solution –
⇒ a : b : c : d
3 : 5 : 5 : 5
4 : 4 : 3 : 3
2 : 2 : 2 : 5
⇒ a : b : c : d = (3 × 4 × 2) : (5 × 4 × 2) : (5 × 3 × 2) : (5 × 3 × 5)
⇒ a : b : c : d = 24 : 40 : 30 : 75
49.If a number x is divided into 3 parts A, B and C, they are in ratio of 2 : 5 : 3. If half of the number is 500. Find thrice of C.
यदि किसी संख्या x को 3 भागों A, B और C में विभाजित किया जाता है, वे 2 : 5 : 3 के अनुपात में हैं। यदि संख्या का आधा 500 है, तो C का तीन गुना ज्ञात कीजिये?
Option”B” is correct
Given:
Half of the number = 500
A : B : C = 2 : 5 : 3
Calculation:
Given number = 2 × 500 = 1000
Let the pats A, B, and C be 2x, 5x, and 3x respectively.
⇒ 2x + 5x + 3x = 1000
⇒ 10x = 1000
⇒ x = 100
C = 3x = 3 × 100 = 300
The value of thrice of C = 3 × C = 900
∴ Thrice of C is 900
50. The boy-girl ratio of a class is 4 ∶ 3. The number of girls scoring above 60% and below 60% is in the ratio 5 ∶ 3. If the total strength of class is 56, how many girls score below 60%?
एक कक्षा के लड़का-लड़की का अनुपात 4 : 3 है। 60% से ऊपर और 60% से नीचे अंक प्राप्त करने वाली लड़कियों की संख्या का अनुपात 5 : 3 में है। यदि कक्षा में छात्रों की कुल संख्या 56 है, तो कितनी लड़कियों ने 60% से कम अंक अर्जित किये हैं?
Option”D” is correct
Total no. of students = 56
Boy-girl ratio = 4 ∶ 3
⇒ Total no. of girls = 3/7 × 56 = 24
Ratio of girls scoring above 60% and below 60% = 5 ∶ 3
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