A gentleman buys every year Bank's cash certificates of value exceeding the last year's purchase by Rs. 300. After 20 years, he finds that the total value of the certificates purchased by him is Rs. 83,000. Find the value of the certificates purchased by him in the 13 year.
Let the value of the certificates purchased in the first year be Rs. a.
The difference between the value of the certificates is Rs. 300 (d = 300).
Since, it follows Arithmetic progression the total value of the certificates after 20 years is given
by Sn = n/2 [2a + (n - 1) d] = 20/2[2a + 19(300)] = 83,000.
By simplifying we get 2a + 5700 = 8300.
Therefore, a = Rs. 1300.
The value of the certificates purchased by him in nth year = a + (n - 1) d.
So, the value of the certificates purchased by him in 13th year = 1300 + (13 - 1) 300 = Rs.4900.
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A, B and C start a business each investing Rs. 20000. After 5 months A withdrew Rs.5000, B withdrew Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69,900 was recorded. Find the share of each.
Ratio of the capitals of A, B and C
= (20000*5+ 15000*7) : (20000*5+16000*7): (20000*5+26000*7)
=205000: 212000 : 282000 = 205:212:282
Therefore, A's share = Rs. ( 69900*205/699) = Rs. 20,500
B's share = Rs. (69900*212/699) = Rs. 21200,
C's share = Rs. (69900*282/699) = Rs. 28200.
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Rs.432 is divided amongst three workers A, B and C such that 8 times A's share is equal to 12 times B's share which is equal to 6 times C's share. How much did A get?
8 times A's share = 12 times B's share = 6 times C's share.
Note that this is not the same as the ratio of their wages being 8 : 12 : 6
In this case, find out the L.C.M of 8, 12 and 6 and divide the L.C.M by each of the above
numbers to get the ratio of their respective shares.
The L.C.M of 8, 12 and 6 is 24.
Therefore, the ratio A:B:C :: 24/8 : 24/12 : 24/6
=> A : B : C :: 3 : 2 : 4
The sum of the total wages = 3x + 2x + 4x = 432 => 9x = 432 or x = 48.
Hence A gets 3 * 48 = Rs. 144.
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Sanjiv started a business by investing Rs. 36000. After 3 months Rajiv joined him by investing Rs. 36000. Out an annual profit of Rs. 37100, find the share of each?
Ratio of their capitals= 36000*12:36000*9 = 4:3
Sanjiv's share= Rs. ( 37100*4/7) = Rs. 21200.
Rajiv's share = Rs. ( 37100*3/7) = Rs.15900.
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A and B enter in to a partnership and A invests Rs. 10,000 in the partnership. At the end of 4 months he withdraws Rs.2000. At the end of another 5 months, he withdraws another Rs.3000. If B receives Rs.9600 as his share of the total profit of Rs.19,100 for the year, how much did B invest in the company?
The total profit for the year is 19100. Of this B gets Rs.9600.
Therefore, A would get (19100 - 9600) = Rs.9500.
The partners split their profits in the ratio of their investments.
Therefore, the ratio of the investments of A : B = 9500 : 9600 = 95 : 96.
A invested Rs.10000 initially for a period of 4 months. Then, he withdrew Rs.2000.
So, his investment has reduced to Rs.8000 (for the next 5 months).
Then he withdraws another Rs.3000. Hence, his investment will stand reduced to Rs.5000
during the last three months.
So, the amount of money that he had invested in the company on a money-month basis
will be = 4 * 10000 + 5 * 8000 + 3 * 5000 = 40000 + 40000 + 15000 = 95000
If A had 95000 money months invested in the company, B would have had 96,000
money months invested in the company (as the ratio of their investments is 95 : 96).
If B had 96,000 money-months invested in the company.
So, he has essentially invested 96000/12 = Rs.8000
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If Rs 510 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets, then their shares are respectively:
A per the question:
A = 2/3 B and B = 1/4 C
=> A/B = 2/3 and B/C = 1/4
Or A:B = 2:3 and B:C = 1:4 = 3:12
=> A:B:C = 2:3:12
So, A's share = 510 * 2/17 = Rs 60
B's share = 510 * 3/17 = Rs 90
C's share = 510 * 12/17 = Rs 360.
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A, B and C started a business with capitals of Rs 8000, Rs 10000 and Rs 12000 respectively. At the end of the year, the profit share of B is Rs 1500. The difference between the profit shares of A and C is?
As per the question:
Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
Given, profit share of B = Rs. 1500
5 parts out of 15 parts = Rs. 1500
Difference between the profit share of (A,C) = 6 - 4 = 2 parts
So, required difference = 2/5 *(1500) = Rs 600
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John told Mark that if Mark gives 1/3rd of his money to him, he will have Rs 75. Mark told John that if john gives 1/2 his money to him, he will have Rs 75. How much money did they have totally?
Anil and suresh started a business with Rs.50,000 and 40,000 respectively. After 6 months Rakesh joined them with capital of Rs.60,000 They got a profit of Rs.6000, then profit of Rakesh is
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