A sum of Rs. 76 is divided among A, B, C in such a way that A gets Rs. 7 more than that what B gets and B gets Rs. 6 more than what C gets. The share of B is:
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Solution
Let money received by C = Rs. x
than money received by B = Rs. (x + 6)
∴ Money received by A = Rs. x + 6 + 7
∴ x + x + 6 + x + 6 + 7 = 76
x = Rs. 19
∴ Money received by B = 19 + 6 = Rs. 25
The value of tan 11° tan 17° tan 45° tan 79° tan 73° is
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Solution
tan 11° tan 17° tan 45° tan 79° tan 73° = tan 11° tan 17° tan 45° cot 11° cot 17°
tan 11° tan 17° tan 45° tan 79° tan 73° = 1
If the side of a square is reduced by 50%, its area will be reduced by:
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Solution
% decrease = 50 + 50 – = 75%
On what sum of money will the difference between SI and CI for 2 years at 5% per annum be equal to Rs. 25 ?
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Solution
Principal = = Rs. 10000
A shopkeeper marks his goods 40% above the cost price. He allows a discount of 5% for cash payment to his customers. He receives Rs. 1064 after paying the discount. His profit is-
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Solution
Profit % = 40 – 5 –
∴ Profit = = Rs. 264
The distance between the centres of two circles having radii 8 cm and 3 cm is 13 cm is 13 cm. The length of the direct common tangent of the two circles is
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Solution
Length of direct common tangent =
= 12 cm
The sum of the internal angles of a regular polygon is 1440°, the number of sides is:
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Solution
Let the number of sides is x
∴ (x – 2) × 180 = 1440
x = 10
If x + y + z = 6, then the value of (x–1)3 + (y–2)3 + (z–3)3 is:
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Solution
x – 1 + y – 2 + z – 3 = x + y + z – 6 = 0
∴ (x – 1)3 + (y – 2)3 + (z – 3)3 = 3(x – 1) (y – 2) (z – 3)
If out of 10 selected students for an examination, 3 were of 20 years age, 4 of 21 years and 3 of 22 years, the average age of the group is:
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Solution
Average Age = = 21 years
The value of
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Solution
= 1 + 1 – 8 × = 0