Ratio, Proportion
- How many sides does a regular polygon have whose interior and exterior angles are in the ratio 2 : 1?
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Let interior angle = I and exterior angle = E
According to questions,I = 2 ⇒ 2E = I.1 or, E = I E 1 2
But I + E = 180°I + I = 180 2 3 I = 180 2 I = 2 × 180 3
I = 120°
We know that each interior angle of a regular polygon of n sides is given byI = n − 2 × 180° n 120° = n − 2 × 180° n ⇒ n − 2 = 120° = 2 n 180° 3
⇒ 3n – 6 = 2n ⇒ n = 6Correct Option: C
Let interior angle = I and exterior angle = E
According to questions,I = 2 ⇒ 2E = I.1 or, E = I E 1 2
But I + E = 180°I + I = 180 2 3 I = 180 2 I = 2 × 180 3
I = 120°
We know that each interior angle of a regular polygon of n sides is given byI = n − 2 × 180° n 120° = n − 2 × 180° n ⇒ n − 2 = 120° = 2 n 180° 3
⇒ 3n – 6 = 2n ⇒ n = 6
- ₹ 600 is divided among A, B and C. ₹ 40 more than (2/5)th of A’ share, ₹ 20 more than (2/7)th of B’s share and ₹ 10 more than (9/17)th of C’s share are all equal. Then A’s share is
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According to the question,
A + B + C = 600 .... (i)
and2A + 40 = 2B + 20 = 9C + 10 5 7 17 ∴ 2A + 40 = 2B + 20 5 7 = 2A + 20 = 2 B 5 7 ∴ B = 7 
2A + 20 
= 7A + 70 2 5 5 Again, 2A + 40 = 9C + 10 5 17 ⇒ 9C = 2A + 30 17 5 ⇒ C = 17 2A + 30 9 5 = 34A + 170 45 3 ∴ A + 7A + 70 = 34A + 170 = 600 5 45 3 ⇒ A + 7A + 34A = 600 − 70 − 170 5 45 3 ⇒ 45A + 63A + 34A 45 = 530 − 170 3 ⇒ 142A = 1590 − 170 = 1420 45 3 3 ⇒ A = 1420 × 45 3 142
= Rs. 150Correct Option: A
According to the question,
A + B + C = 600 .... (i)
and2A + 40 = 2B + 20 = 9C + 10 5 7 17 ∴ 2A + 40 = 2B + 20 5 7 = 2A + 20 = 2 B 5 7 ∴ B = 7 2A + 20 = 7A + 70 2 5 5 Again, 2A + 40 = 9C + 10 5 17 ⇒ 9C = 2A + 30 17 5 ⇒ C = 17 2A + 30 9 5 = 34A + 170 45 3 ∴ A + 7A + 70 = 34A + 170 = 600 5 45 3 ⇒ A + 7A + 34A = 600 − 70 − 170 5 45 3 ⇒ 45A + 63A + 34A 45 = 530 − 170 3 ⇒ 142A = 1590 − 170 = 1420 45 3 3 ⇒ A = 1420 × 45 3 142
= Rs. 150
- A, B and C invested ₹ 13,000, ₹ 17,000 and ₹ 5,000 respectively in a business. At the end of the year, they earn a profit of ₹ 1,400. B’s share of profit is
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Ratio of the equivalent capitals of A, B and C for 1 month
= 13000 × 12 : 17000 × 12 : 5000 × 12
= 13 : 17 : 5
Sum of the terms of ratio
= 13 + 17 + 5 = 35
Total profit = Rs. 1400∴ B’s share = Rs. 17 × 1400 = Rs. 680 35 Correct Option: A
Ratio of the equivalent capitals of A, B and C for 1 month
= 13000 × 12 : 17000 × 12 : 5000 × 12
= 13 : 17 : 5
Sum of the terms of ratio
= 13 + 17 + 5 = 35
Total profit = Rs. 1400∴ B’s share = Rs. 17 × 1400 = Rs. 680 35
- ₹ 1980 is divided among A, B and C so that half of A’s part, one-third of B’s part and onesixth of C’s part are equal. Then B’s part is
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According to the question,
A = B = C 2 3 6
∴ A : B : C = 2 : 3 : 6
Sum of the terms of ratio
= 2 + 3 + 6 = 11
Total amount = Rs. 1980∴ B’s share = Rs. 3 × 1980 = Rs. 450 11 Correct Option: A
According to the question,
A = B = C 2 3 6
∴ A : B : C = 2 : 3 : 6
Sum of the terms of ratio
= 2 + 3 + 6 = 11
Total amount = Rs. 1980∴ B’s share = Rs. 3 × 1980 = Rs. 450 11
- A sum of Rs. 15525 is divided among Sunil, Anil and Jamil such that if Rs. 22, Rs. 35 and Rs. 48 be diminished from their shares respectively, their remaining sums shall be in the ratio 7 : 10 : 13. What would have been the ratio of their sums if Rs. 16, Rs. 77 and Rs. 37 respectively were added to their original shares?
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According to the question,
Amount to be distributed in the ratio 7 : 10 : 13
= Rs. (15525 – 22 – 35 – 45)
= Rs. 15420
Sum of the terms of ratio
= 7 + 10 + 13 = 30Sunil’s share = Rs. 7 × 15420 = Rs. 3598 30 Anil’s share = Rs. 10 × 15420 = Rs. 5140 30 Jamil’s share = Rs. 13 × 15420 = Rs. 6682 30
Ratio after respective increase in each share
= (3598 + 22 + 16) : (5140 + 35 + 77) : (6682 + 48 + 37)
= 3636 : 5252 : 6767
= 36 : 52 : 67Correct Option: C
According to the question,
Amount to be distributed in the ratio 7 : 10 : 13
= Rs. (15525 – 22 – 35 – 45)
= Rs. 15420
Sum of the terms of ratio
= 7 + 10 + 13 = 30Sunil’s share = Rs. 7 × 15420 = Rs. 3598 30 Anil’s share = Rs. 10 × 15420 = Rs. 5140 30 Jamil’s share = Rs. 13 × 15420 = Rs. 6682 30
Ratio after respective increase in each share
= (3598 + 22 + 16) : (5140 + 35 + 77) : (6682 + 48 + 37)
= 3636 : 5252 : 6767
= 36 : 52 : 67
