Divide Rs 1312 into three parts in the ratio such that first part is 2/3 of the second and the ratio between second and third parts is 4:7.
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The ratio of 1st part to 2nd part = 2/3 OR 2:3 ........... (i)
The ratio of the 2nd part to the 3rd part = 4:7 ............. (ii)
Multiply (i) by 4 and (ii) by 3
The ratio of 1st part to 2nd part = 8:12
The ratio of 2nd to 3rd part = 12:21 (Now the ratio representing the 2nd part is equal in (i) and (ii)
Meaning the ratio of the 1st:2nd:3rd = 8:12:21
Sum of the ratios = 8+12+21 = 41
1st part = 8/41 x 1312 = Rs. 256
2nd part = 12/41 x 1312 = Rs. 384
3rd part = 21/41 x 1312 = Rs. 672
The ratio of the 2nd part to the 3rd part = 4:7 ............. (ii)
Multiply (i) by 4 and (ii) by 3
The ratio of 1st part to 2nd part = 8:12
The ratio of 2nd to 3rd part = 12:21 (Now the ratio representing the 2nd part is equal in (i) and (ii)
Meaning the ratio of the 1st:2nd:3rd = 8:12:21
Sum of the ratios = 8+12+21 = 41
1st part = 8/41 x 1312 = Rs. 256
2nd part = 12/41 x 1312 = Rs. 384
3rd part = 21/41 x 1312 = Rs. 672
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