111. Rs. 750 are divided among A, B and C in such a manner that A : B = 5 : 2 and B : C = 7 : 13, What is A’s share? 750 रुपये को A, B, और C के बीच इस तरह से बांटा गया है कि A : B = 5 : 2 और B : C = 7 : 13, A का हिस्सा कितना है?
Option”D” is correct
Rs. 750 are divided among A, B and C in such a manner that A : B = 5 : 2 and B : C = 7 : 13
Formula Used:
If A : B = a : b1 and B : C = b2 : c, then A : B : C = ab2 : b1b2 : b1c
Calculation:
⇒ A : B : C = 35 : 14 : 26
Let the share of A, B and C be 35x, 14x and 26x respectively
⇒ A’s share = 35x/(35x + 14x + 26x) × 750
⇒ A’s share = (35/75) × 750
⇒ A’s share = Rs. 350
∴ required A’s share = Rs. 350
112. If a : b = 2 : 3, b : c = 6 : 10, c : d = 20 : 30 and d : e = 60 : 80 then what is a : e? यदि a : b = 2 : 3, b : c = 6 : 10, c : d = 20 : 30 तथा d : e = 60 : 80 तो a : e क्या है?.
Option”C” is correct
Given:
a : b = 2 : 3
b : c = 6 : 10
c : d = 20 : 30
d : e = 60 : 80
Calculation:
Let e = 80p
d = 60p
c : d = 20 : 30
∴ c = (60p/30) × 20
= 40p
b : c = 6 : 10
∴ b = (40p/10) × 6
= 24p
a : b = 2 : 3
∴ a = (24p/3) × 2
= 16p
∴ a : e = 16p : 80p
a : e = 1 : 5
113. Ratio of women and men in an office is 2 : 3 and the ratio of salary of each women and men is 7 : 6. If the difference of total salary disbursed to all the men and all the women is Rs. 67200, then find the amount of salary disbursed to all the women. एक कार्यालय में महिलाओं और पुरुषों का अनुपात 2 : 3 है और प्रत्येक महिला और पुरुष के वेतन का अनुपात 7 : 6 है। यदि सभी पुरुषों और सभी महिलाओं को संवितरित कुल वेतन का अंतर 67200 रुपये है, तब सभी महिलाओं को संवितरित वेतन की धनराशि ज्ञात कीजिये।
Option”D” is correct
Ratio of women and men in an office is 2 : 3
Suppose the number of women and men is 2x And 3x respectively;
Ratio of salary = 7 : 6
Suppose the amount of salary of women and men is 7y And 6y respectively;
∴ Total amount disbursed to all the women = 14xy
Total amount disbursed to all the men = 18xy
∴ 18xy – 14xy = 67200
⇒ xy = 16800
∴ Total amount disbursed to all the women = 14xy = Rs. 235200
114. Some people used rum, vodka and juice to prepare cocktail in a party. The quantity of Rum and Vodka together was 3750 ml. If the ratio of quantities of rum and vodka was 2 : 3 and the ratio of rum and juice used was 6 : 13, then find the total quantity of cocktail that has been prepared. कुछ व्यक्ति एक पार्टी में कॉकटेल बनाने के लिए रम, वोडका और जूस का उपयोग करते हैं। रम और वोडका की एकत्रित मात्रा 3750 मिली है। यदि रम और वोडका की मात्रा का अनुपात 2 : 3 और रम और जूस की मात्रा का अनुपात 6 : 13 है, तब निर्मित कॉकटेल की कुल मात्रा ज्ञात कीजिये।
Option”A” is correct
Rum : Vodka = 2 : 3 and
Rum : Juice = 6 : 13
∴ Rum : Vodka : Juice = 6 : 9 : 13
Since the quantity of Rum and Vodka together was 3750 ml;
Total quantity of Rum, Vodka and Juice = Quantity of Cocktail = x ml
∴ [(6 + 9)/28] × x = 3750
⇒ x = 7000 ml
∴ Total quantity of cocktail = 7000 ml
115. Find the compound ratio of 4 ∶ 9, 6 ∶ 5 and 10 ∶ 3. 4 ∶ 9, 6 ∶ 5 और 10 ∶ 3 का मिश्रित अनुपात ज्ञात कीजिये।
Option”B” is correct
The compound ratios of ratios a ∶ b, c ∶ d and e ∶ f is given as ace ∶ bdf
116. The ratio of theme park entrance fee for adults and children is 9 ∶ 4 and for particular day ratio of number of adult visitor and number of children is 8 ∶ 13, for that particular day total earning from children visitors is Rs. 26000. Find the difference in amount collected from adult visitors and children visitors. एक थीम पार्क में वयस्कों और बच्चों के प्रवेश शुल्क का अनुपात 9 ∶ 4 है और किसी विशेष दिवस पर वयस्क आगंतुकों और बच्चों की संख्या का अनुपात 8 : 13 है, उस विशेष दिन आये हुए बच्चों से कुल कमाई 26000 रूपये थी। आए हुए वयस्क और बच्चों से एकत्रित होने वाली राशि का अंतर ज्ञात कीजिए।
Option”B” is correct
Given,
⇒ Ratio of fee for adults and children = 9 ∶ 4
⇒ Ratio of number of adult visitors and children = 8 ∶ 13
Using compound ratio,
⇒ Ratio of earning from adult visitors and children = (9 × 8) ∶ (4 × 13) = 18 ∶ 13
Given,
⇒ Earning from children = 26000
Then,
⇒ Total earning for that day = 26000 × {(18 + 13)/ 13} = 62000
117. The compound ratio of (8 ∶ a), (3 ∶ 32) and (b ∶ 27) is 4 ∶ 81. Find the value of (2a – b) ∶ (a + b). (8 ∶ a), (3 ∶ 32) और (b ∶ 27) का मिश्र अनुपात 4 ∶ 81 है। (2a – b) ∶ (a + b) का मान ज्ञात कीजिए।
Option”B” is correct
Given,
Compound ratio of 8 ∶ a, 3 ∶ 32 and b ∶ 27
= (8 × 3 × b) ∶ (a × 32 × 27) = b ∶ 36a
Then,
⇒ 4 ∶ 81 = b ∶ 36a
⇒ a ∶ b = 9 ∶ 16
Given,
⇒ ? = (2a – b) ∶ (a + b)
⇒ ? = (2a/b – 1) / (a/b + 1)
⇒ ? = [(9 – 8)/8] / [(9 + 16)/16]
⇒ ? = (1/8) / (25/16)
⇒ ? = 2/25
⇒ ? = 2 ∶ 25
118.If compound ratio of (16 : N), (M : 21) and (7 : 8) is 10 : 3, then find the compound ratio of (M : 7) and (14 : N). यदि (16 : N), (M : 21) और (7 : 8) का मिश्रित अनुपात 10 : 3 है, तो (M : 7) और (14 : N) का मिश्रित अनुपात ज्ञात कीजिये।
Option”B” is correct
Given,
Using compound ratio formula,
⇒ 10 : 3 = (16 × M × 7) : (N × 21 × 8)
⇒ 10 : 3 = 2M : 3N
⇒ M : N = 5 : 1
Then,
Compound ratio of (M : 7) and (14 : N)
= (M × 14) : (7 × N)
= 10 : 1
119.If the compound ratio of ratios (2x – y) ∶ (x + y) and (x – 2y) ∶ (x – y) is 2 ∶ 1, find the value of x ∶ y. यदि अनुपात (2x – y) : (x + y) और (x – 2y) : (x – y) का मिश्र अनुपात 2 : 1 है, तो x : y का मान ज्ञात कीजिए।
Option”D” is correct
As we know, the compound ratio of ratios a ∶ c and b ∶ d is ab ∶ cd
⇒ Compound ratio of given ratios = [(2x – y)(x – 2y)] ∶ [(x + y)(x – y)] = 2 ∶ 1
⇒ 2x2 – 4xy – xy + 2y2 = 2(x2 – y2)
⇒ 2x2 – 5xy + 2y2 = 2x2 – 2y2
⇒ 4y2 = 5xy
⇒ 4y = 5x
⇒ x/y = 4/5
∴ Required ratio = x ∶ y = 4 ∶ 5
120. Three partners A, B and C, share profit profits and losses in the ratio of 3 ∶ 4 ∶ 7. If the profit for the year before charging 30% tax is Rs. 1,10,166 what is B’s share of profit after tax? तीन साझेदार A, B और C लाभ और हानि को 3 ∶ 4 : 7 के अनुपात में साझा करते हैं। यदि 30% कर लगाने से पहले वर्ष का लाभ 1,10,166 रूपये है, तो कर लगाने के बाद B के लाभ का हिस्सा कितना होगा?
Option”A” is correct
Profit for the year before charging 30% tax = P = Rs. 110166
∴ Profit for the year after charging 30% tax = (100 – 30)% of P = 70% of P
Total share = 3 + 4 + 7 = 14
⇒ B’s share of profit after tax = (4/14) × (70/100) × 110166 = Rs. 22033.2
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